Princeton University - The Return of Monetary Rulesassets.press.princeton.edu/chapters/s7603.pdfCHAPTER 1 The Return of Monetary Rules Ifitwereinourpowertoregulatecompletelythepricesystemofthe

C H A P T E R 1

The Return of Monetary Rules

If it were in our power to regulate completely the price system of thefuture, the ideal position . . . would undoubtedly be one in which, with-out interfering with the inevitable variations in the relative prices of com-modities, the general average level of money prices . . . would be perfectlyinvariable and stable.And why should not such regulation lie within the scope of practical

politics? . . . Attempts by means of tariffs, state subsidies, export bounties,and the like, to effect a partial modification of the natural order of [rela-tive prices] almost inevitably involve some loss of utility to the community.Such attempts must so far be regarded as opposed to all reason. Absoluteprices on the other hand—money prices—are a matter in the last analysisof pure convention, depending on the choice of a standard of price which itlies within our own power to make.

—Knut WicksellInterest and Prices, 1898, p. 4

The past century has been one of remarkable innovation in the world’smonetary systems. At the turn of the twentieth century, it was taken forgranted by practical men that the meaning of a monetary unit should beguaranteed by its convertibility into a specific quantity of some preciousmetal. Debates about monetary policy usually concerned the relative advan-tages of gold and silver standards or the possibility of a bimetallic standard.But through fits and starts, the world’s currencies have come progressivelyto bemore completely subject to “management” by individual central banks.Since the collapse of the Bretton Woods system of fixed exchange rates inthe early 1970s, the last pretense of a connection of the world’s currenciesto any real commodity has been abandoned. We now live instead in a worldof pure “fiat” units of account, where the value of each depends solely uponthe policies of the particular central bank with responsibility for it.This has brought both opportunities and challenges. On the one hand,

vagaries of the market for gold or some other precious metal no longercause variations in the purchasing power of money, with their disruptionsof the pattern of economic activity. The recognition that the purchasing

1

2 Chapter 1. The Return of Monetary Rules

power of money need not be dictated by any “natural” market forces andis instead a proper subject of government regulation, as proposed by themonetary reformer Knut Wicksell a century ago, should in principle makepossible greater stability of the standard of value, facilitating contractingand market exchange. At the same time, the responsibilities of the world’scentral banks are more complex under a fiat system than they were whenthe banks’ tasks were simply to maintain convertibility of their respectivenational currencies into gold, and it was not immediately apparent how thebanks’ new freedom should best be used. Indeed, during the first decadeof the new regime, the policies of many industrial nations suffered from atendency toward chronic inflation, leading to calls from some quarters inthe 1980s for a return to a commodity standard.This has not proven to be necessary. Instead, since the 1980s the cen-

tral banks of the major industrial nations have been largely successful atbringing inflation down to low and fairly stable levels. Nor does this seemto have involved any permanent sacrifice of other objectives. For example,real GDP growth has been if anything higher on average, and certainly morestable, since inflation was stabilized in the United States. Somewhat para-doxically, this period of improved macroeconomic stability has coincidedwith a reduction, in certain senses, in the ambition of central banks’ effortsat macroeconomic stabilization. Banks around the world have committedthemselves more explicitly to relatively straightforward objectives with re-gard to the control of inflation, and have found when they do so that notonly is it easier to control inflation than previous experience might havesuggested, but that price stability creates a sound basis for real economicperformance as well.What appears to be developing, then, at the turn of another century, is

a new consensus in favor of a monetary policy that is disciplined by clearrules intended to ensure a stable standard of value, rather than one thatis determined on a purely discretionary basis to serve whatever ends mayseemmost pressing at any given time. Yet the new monetary rules are not soblindly mechanical as the rules of the gold standard, which defined mone-tary orthodoxy a century ago. They are instead principles of systematic con-duct for institutions that are aware of the consequences of their actions andtake responsibility for them, choosing their policies with careful attention towhat they accomplish. Indeed, under the current approaches to rule-basedpolicymaking, more emphasis is given to explicit commitments regardingdesired economic outcomes, such as a target rate of inflation, than to partic-ular technical indicators that the central bank may find it useful to monitorin achieving that outcome.The present study seeks to provide theoretical foundations for a rule-

based approach to monetary policy of this kind. The development of sucha theory is an urgent task, for rule-based monetary policy in the spirit

Chapter 1. The Return of Monetary Rules 3

that I have described is possible only when central banks can develop aconscious and articulate account of what they are doing. It is necessary inorder for them to know how to act systematically in a way that can serve theirobjectives, which are nowdefined in terms of variables that aremuch furtherremoved from their direct control. It is also necessary in order for them tobe able to communicate the nature of their systematic commitments to thepublic, despite the absence of suchmechanical constraints as a commitmentto exchange currency for some real commodity. As I explain below, theadvantages of a sound monetary policy are largely dependent upon thepolicy’s being understood and relied upon by the private sector in arrangingits affairs.There can be little doubt that the past decade has seen amarked increase

in the self-consciousness of central banks about the way in which they con-duct monetary policy and in the explicitness of their communication withthe public about their actions and the considerations upon which they arebased. A particularly important development in this regard has been theadoption of “inflation targeting” as an approach to the conduct ofmonetarypolicy by many of the world’s central banks in the 1990s.1 As I subsequentlydiscuss in more detail, this approach (best exemplified by the practices ofsuch innovators as the Bank of England, the Bank of Canada, the ReserveBank of New Zealand, and the Swedish Riksbank) is characterized not onlyby public commitment to an explicit target, but also by a commitment to ex-plain the central bank’s policy actions in terms of a systematic decisionmak-ing framework that is aimed at achieving this target. This has led to greatlyimproved communication with the public about the central bank’s interpre-tation of current conditions and the outlook for the future, notably throughthe publication of detailed Inflation Reports. It has also involved fairly explicitdiscussion of the approach that they follow in deliberating about policy ac-tions and, in some cases, even publication of the model or models used inproducing the forecasts that play a central role in these deliberations. As aconsequence, these banks in particular have found themselves in need of aclear theory of how they can best achieve their objectives and have playedan important role in stimulating reflection on this problem.It is true that the conceptual frameworks proposed by central banks

to deal with their perceived need for a more systematic approach to pol-icy were, until quite recently, largely developed without much guidancefrom the academic literature on monetary economics. Indeed, the centralquestions of practical interest for the conduct of policy—how should cen-tral banks decide about the appropriate level of overnight interest rates?how should monetary policy respond to the various types of unexpecteddisturbances that occur?—had in recent decades ceased to be considered

1. See, e.g., Bernanke et al. (1999) for a thorough discussion of this development.


suitable topics for academic study. Reasons for this included the trenchantcritique of traditional methods of econometric-policy evaluation by Lucas(1976); the critique of the use of conventional methods of optimal controlin the conduct of economic policy by Kydland and Prescott (1977); and thedevelopment of a new generation of quantitative models of business fluc-tuations (“real-business-cycle theory”) with more rigorous microeconomicfoundations, but which implied no relevance of monetary policy for eco-nomic welfare.Nonetheless, recent developments, to be discussed in detail in this vol-

ume, have considerably changed this picture. The present study seeks toshow that it is possible to use the tools of modern macroeconomic theory—intertemporal equilibrium modeling, taking full account of the endogene-ity of private-sector expectations—to analyze optimal interest-rate setting ina way that takes the concerns of central bankers seriously, while simulta-neously taking account of the “New Classical” critique of traditional policy-evaluation exercises. In this way, the basic elements are presented of a theorythat can provide the groundwork for the kind of systematic approach to theconduct of monetary policy that many central banks are currently seekingto develop. In the present chapter, I review some of the key features of thistheory, as preparation for the more systematic development that begins inChapter 2.

1 The Importance of Price Stability

A notable feature of the new rule-based approaches to monetary policy isthe increased emphasis given to a particular policy objective: maintaining alow and stable rate of inflation. This is most obvious in the case of countrieswith explicit inflation targets. But it also seems to characterize recent policyin the United States as well, where the past decade has seen unusual stabilityof the inflation rate and many econometric studies have found evidence ofa stronger Fed reaction to inflation variations. (See further discussion ofrecent U.S. policy in Section 4.1.)Yet the justification of such an emphasis from the standpoint of economic

theory may not be obvious. Standard general-equilibriummodels—and theearliest generation of quantitative equilibrium models of business fluctua-tions, the real-business-cyclemodels of the 1980s—indicate that the absolutelevel of prices should be irrelevant for the allocation of resources, whichdepends only on relative prices. Traditional Keynesian macroeconometricmodels, of course, imply otherwise: Variations in the growth rate of wagesand prices are found to be associated with substantial variations in eco-nomic activity and employment. Yet the existence of such “Phillips-curve”relations has typically been held to imply that monetary policy should be

1. The Importance of Price Stability 5

used to achieve output or employment goals, rather than giving priority toprice stability.The present study argues instead for a different view of the proper goals

of monetary policy. Its use to stabilize an appropriately defined price in-dex is in fact an important end toward which efforts should be directed—atleast to a first approximation, it should be the primary aim of monetarypolicy. But this is not, as proponents of inflation targeting sometimes argue,because variations in the rate of inflation have no real effects. Rather, it isexactly because instability of the general level of prices causes substantialreal distortions—leading to inefficient variation both in aggregate employ-ment and output and in the sectoral composition of economic activity—thatprice stability is important.Moreover, the existence of predictable real effects of shifts in monetary

policy need not imply that policy should be based primarily on a calcu-lation of its effects on output or employment. For the efficient aggregatelevel and sectoral composition of real activity is likely to vary over time, as aresult of real disturbances of a variety of types. The market mechanism per-forms a difficult computational task—much of the time, fairly accurately—in bringing about a time-varying allocation of resources that responds tothese changes in production and consumption opportunities. Because ofthis, variation over time in employment and output relative to some smoothtrend cannot in itself be taken to indicate a failure of proper market func-tioning. Instead, instability of the general level of prices is a good indicatorof inefficiency in the real allocation of resources—at least when an appro-priate price index is used—because a general tendency of prices to movein the same direction (either all rising relative to their past values or allfalling) is both a cause and a symptom of systematic imbalances in resourceallocation.This general vision is in many respects an attempt to resurrect a view that

was influential among monetary economists prior to the Keynesian revolu-tion. It was perhaps best articulated by the noted Swedish economic theoristKnut Wicksell at the turn of the previous century, along with his followersin the “Stockholm school” of the interwar period (such as Erik Lindahl andGunnarMyrdal) and others influenced byWicksell’s work, such as FriedrichHayek. However, these authors developed their insights without the benefitof either modern general-equilibrium theory2 or macroeconometric mod-eling techniques, so that it may be doubted whether Wicksellian theory can

2. Of course, Wicksell and his followers were quite familiar with Walrasian general-equilib-rium theory and used it as a starting point for their own thought. But at the time, general-equilibrium theory meant a static model of resource allocation, not obviously applicable to theproblems of intertemporal resource allocation with which they were primarily concerned. See,e.g., Myrdal (1931, chap. 2, sec. 4, and chap. 3, sec. 5).


provide a basis for the kind of quantitative policy analysis in which a mod-ern central bank must engage—and which has become only more essentialgiven current demands for public justification of policy decisions. This bookseeks to provide theoretical foundations for the view just sketched that meetmodern standards of conceptual rigor and are capable of elaboration in aform that can be fit to economic time series.

1.1 Toward a New “Neoclassical Synthesis”

The approach to monetary policy proposed here builds upon advances inthe analysis of economic fluctuations and, in particular, of the monetarytransmission mechanism over the past few years.3 The models analyzed inthis volume differ in crucial respects from the first two generations of equi-librium business-cycle models, namely, the New Classical models that Lucas(1972) took as a starting point and the real-business-cycle (RBC) modelspioneered by Kydland and Prescott (1982) and Long and Plosser (1983).Neither of these early illustrations of the possibility of rigorous intertem-poral general-equilibrium analysis of short-run fluctuations contained ele-ments that would make them suitable for the analysis of monetary policy.While the Lucas model allows for real effects of unexpected variations inmonetary policy (modeled as stochastic variation in the growth rate of themoney supply), it implies that any real effects of monetary policy must bepurely transitory and that monetary disturbances should have no real ef-fects to the extent that their influence on aggregate nominal expenditurecan be forecast in advance. Yet, as shown Chapter 3, VAR evidence on theeffects of identified monetary policy shocks is quite inconsistent with thesepredictions. Rather, these effects on aggregate nominal expenditure areforecastable at least 6 months in advance on the basis of federal funds ratemovements, whereas the (similarly delayed) effects on real activity are sub-stantial and persist for many quarters. Nor is this empirical failure of themodel one of minor import for the analysis of monetary policy. The con-clusion that only unanticipated monetary policy can have real effects leadsfairly directly to the skeptical conclusions of Sargent and Wallace (1975)about the necessary ineffectiveness of any attempt to use monetary policyto stabilize real activity.The RBC models of the 1980s offered a very different view of the typical

nature of short-run fluctuations in economic activity. But the classic modelsin this vein similarly imply no scope at all for monetary stabilization policybecause real variables aremodeled as evolving in complete independence ofany nominal variables. Monetary policy is thus (at least implicitly) assumed

3. Useful surveys of recent developments include Goodfriend and King (1997) and Gali(2001).


to be of no relevance as far as fluctuations in real activity are concerned.Since neither the empirical evidence from VAR studies nor the practicalexperience of central bankers supports this view, I am reluctant to discussthe nature of desirable monetary policy rules using models of this kind.Chapters 3 through 5 review a more recent literature that has shown,

instead, how one can develop models with equally rigorous foundations inintertemporal optimizing behavior that allow amore realistic account of thereal effects of monetary disturbances. These models also imply that system-atic monetary policy can make a substantial difference for the way that aneconomy responds to real disturbances of all sorts, and this is actually theprediction that is of greatest importance for the concerns here. VAR mod-els typically do not imply that a large part of the variance of fluctuations inreal activity should be attributed to monetary policy shocks—that is, to thepurely random component of central-bank interest-rate policy. Moreover, inany event, one does not really need to understand exactly what the effectsof such shocks are, since under almost any view it is desirable to eliminatesuch shocks (i.e., to render monetary policy predictable) to the greatestextent possible. (Here, I discuss the ability of the models being proposed toaccount for evidence with regard to the effects of such shocks only becausethis is the aspect of the effects of monetary policy that can be empiricallyidentified under relatively weak, and hence more convincing, identifying as-sumptions.)On the other hand, I am very interested in what amodel impliesabout the way in which alternative systematic monetary policies determinethe effects of real disturbances. The question of practical importance in cen-tral banking is never “should we create some random noise this month?,”but rather “does this month’s news justify a change in the level of interestrates?” To think about this, one needs to understand the consequences ofdifferent types of possible monetary responses to exogenous disturbances.The key to obtaining less trivial consequences of systematicmonetary pol-

icy in the models proposed here is the assumption that prices and/or wagesare not continually adjusted, but remain fixed for at least short periods (afew months, or even a year) at a level that was judged desirable at an earliertime. However, this postulate does not mean accepting the need for me-chanical models of wage and price adjustment of the kind that were at theheart of the Keynesianmacroeconometric models of the 1960s. Rather thanpostulating that prices or wages respond mechanically to some measure ofmarket disequilibrium, they are set optimally, that is, so as to best serve theinterests of the parties assumed to set them, according to the informationavailable at the time they are set. The delays involved before the next timethat prices are reconsidered (or perhaps, before a newly chosen price takeseffect) are taken here to be an institutional fact, just like the available pro-duction technology. However, the resulting constraints are taken accountof by the decisionmakers who set them. Thus the assumed “stickiness” of


prices implies that when they are reconsidered, they are set in a forward-looking manner, on the basis of expectations regarding future demand andcost conditions, and not simply in response to current conditions. As a re-sult, expectations turn out to be a crucial factor in the equilibrium relationbetween inflation and real activity (as argued by Phelps and Friedman inthe 1960s). Under certain special assumptions, described in Chapter 3, therelation is of exactly the form assumed in the New Classical literature: Devi-ations of output from its “natural rate” are proportional to the unexpectedcomponent of inflation. However, this is not true more generally. Othermodels, which I would judge to be more realistic, also lead to “expectations-augmented Phillips-curve” relations of a sort, but not of the precise sort thatimplies that anticipated monetary policy cannot have real effects.It is also important to note that the emphasis here upon nominal rigidi-

ties does not in any way mean ignoring the real factors in business fluc-tuations stressed by RBC theory. One important achievement of the RBCliterature has been to show that the equilibrium level of output can eas-ily be disturbed by real disturbances of many sorts—variations in the rateof technical progress, variations in government purchases, changes in taxrates, or different kinds of shifts in tastes. I do not want to abstract fromthe existence of such disturbances in the proposed models. After all, it isonly the existence of real disturbances (i.e., disturbances other than thoseoriginating from randomness in monetary policy itself) that gives rise tonontrivial questions about monetary policy, and I strive to obtain resultsthat remain valid for as broad a class of possible disturbances as possible.Of course, the predicted effects of real disturbances are not necessarily thesame in the models presented here as in RBC theory, which, in its classicform, assumes complete flexibility of both wages and prices. Rather, in thesemodels, the predicted effects of real disturbances depend on the nature ofmonetary policy.Nonetheless, the predicted evolution of real variables under complete

wage and price flexibility—the topic studied in RBC theory—represents animportant benchmark in the theory developed here. The level of outputthat would occur in an equilibrium with flexible wages and prices, givencurrent real factors (tastes, technology, government purchases)—what iscalled the “natural rate” of output, following Friedman (1968)—turns outto be a highly useful concept, even if the present theory does not imply thatthis is the actual level of output, regardless of monetary policy. It is the gapbetween actual output and this natural rate, rather than the level of outputas such (or output relative to trend) that is related to inflation dynamicsin a properly specified Phillips-curve relation, as I show in Chapter 3. It isalso this concept of the output gap to which interest rates should respondif a “Taylor rule” is to be a successful approach to inflation stabilization, as Idiscuss in Chapter 4; it is this concept of the output gap thatmonetary policy


should aim to stabilize in order to maximize household welfare, as shown inChapter 6; and it is this concept of the output gap to which optimal interest-rate rules and/or optimal inflation targets should respond, as shown inChapter 8. From the point of view of any of these applications, the fact thatthe natural rate of output may vary at business-cycle frequencies, as arguedin the RBC literature, is of tremendous practical importance. I am also quiteinterested in the consequences of time variation in what Wicksell (1898)called the “natural rate of interest”—the equilibrium real rate of interestin the case of flexible wages and prices, given current real factors.4 Onceagain, RBC theory has a great deal to tell us about the kind of factors thatshould cause the natural rate of interest to vary. Hence RBC theory, whencorrectly interpreted, constitutes an important building block of the theoryto be developed here.It is for this reason that Goodfriend and King (1997) speak of models of

this kind as representing a “new neoclassical synthesis,” in the spirit of thesynthesis between Keynesian short-run analysis and neoclassical long-runanalysis proposed by Hicks and Samuelson. In the modern, more explic-itly dynamic version of such a synthesis, the neoclassical theory (i.e., RBCtheory) defines not a static “long-run equilibrium” but rather a dynamicpath that represents a sort of virtual equilibrium for the economy at eachpoint in time—the equilibrium that one would have if wages and prices werenot in fact sticky. The evolution of the virtual equilibrium matters becausethe gaps between actual quantities and their virtual equilibrium values areimportant measures of the incentives for wage and price adjustment andhence determinants of wage and price dynamics.At the same time, the stickiness of prices and/or wages implies that short-

run output determination can be understood in a manner reminiscent ofKeynesian theory. Indeed, the basic analytical framework in this study hasthe structure of a simple model consisting of an “IS equation,” a mone-tary policy rule, and an “AS equation.” (The monetary policy rule—whichI often suppose is something similar to a Taylor rule—replaces the “LMequation” of Hicksian pedagogy, since for the most part I am not interested

4. This is of course the origin of the natural rate terminology—Friedman’s (1968) conceptof a “natural rate of unemployment” appealed to an analogy with Wicksell’s “natural rate ofinterest,” a concept with which his readers were presumed to be familiar. Nowadays, manyreaders are more familiar with Friedman’s concept and find the natural rate of interest mosteasy to understand as an analogy with Friedman’s natural rate. In fact, Wicksell was also anearly proponent of the “natural rate hypothesis” enunciated in Friedman’s address. “Thosepeople who prefer a continually upward moving to a stationary price level forcibly remind oneof those who purposely keep their watches a little fast so as to be more certain of catchingtheir trains. But to achieve their purpose they must not be conscious . . . of the fact that theirwatches are fast; otherwise they become accustomed to take the extra fewminutes into accountand so after all, in spite of their artfulness, arrive too late” (Wicksell, 1898, pp. 3–4).


here in the consequences of monetary targeting.) Nonetheless, even forpurposes of “short-run” analysis, the proposed model is less static than anold-fashioned Keynesian model; in particular, expectations will be crucial el-ements in its structural relations (e.g., its “intertemporal IS relation”), sothat anything that causes a change in expectations should shift them.The inclusion of significant forward-looking terms in the key structural

relations has substantial consequences for the analysis of the character ofoptimal policy, just as Lucas (1976) argued, even if the consequences arenot necessarily the ones suggested in the New Classical literature. For exam-ple, estimated IS equations in traditional macroeconometric models oftenindicate an effect of lagged rather than current interest rates on aggregatedemand, since the coefficients on lagged rates are found to be more signifi-cant than those on a current interest rate in the case of a regression seekingto explain aggregate real expenditure in terms of observable variables. Onthe other hand, in the optimization-based model estimated by Rotembergand Woodford (1997), the observed delay in the effects of an interest-rateinnovation on real GDP is explained by an assumption that the interest-sensitive component of private spending is predetermined, though chosenin a forward-looking way. Thus current aggregate demand is assumed todepend on past expectations of current and future interest rates, rather thanon past interest rates.Econometrically, the two hypotheses are not easily distinguished, given

the substantial serial correlation of observed interest rates. Yet the secondhypothesis, I would argue, has a much simpler logic in terms of the optimaltiming of expenditure, once one grants the hypothesis of predeterminationof spending decisions (just as with pricing decisions). Moreover, the spec-ification assumed matters greatly for one’s conclusions about the conductof policy. If expenditure is really affected solely by lagged interest rates, itbecomes important for the central bank to adjust interest rates in responseto its forecast of how it would like to affect aggregate demand at a laterdate; “preemptive” actions are essential. If instead only past expectationsof current and future interest rates matter, then unforecastable interest-ratemovements will not affect demand, so that immediate responses to news willserve no purpose. It will then be important for interest rates to continue torespond to the outlook that had been perceived in the past, even if more re-cent news has substantially modified the bank’s forecasts. This inertial char-acter of optimal interest-rate policy is discussed further in Chapters 7 and 8.

1.2 Microeconomic Foundations and Policy Analysis

I consider the development of a model of the monetary transmission mech-anism with clear foundations in individual optimization to be important fortwo reasons: It allows us to evaluate alternative monetary policies in a way


that avoids the flaw in policy evaluation exercises using traditional Keynes-ian macroeconometric models stressed by Lucas (1976); and the outcomesresulting from alternative policies can be evaluated in terms of the prefer-ences of private individuals that are reflected in the structural relations ofone’s model.Lucas (1976) argued that traditional policy evaluation exercises using

macroeconometric models were flawed by a failure to recognize that the re-lations typically estimated—a “consumption equation,” a “price equation,”and so on—were actually (at least under the hypothesis of optimizing be-havior by households and firms) reduced-form rather than truly structuralrelations. In particular, in the estimated equations, expectations regardingfuture conditions (future income in the case of consumers and future costsand future demand in the case of pricesetters) were proxied for by cur-rent and lagged observable state variables. But the correlation of expecta-tions with those observables ought to be expected to change in the case ofa change in the government’s policy rule, as contemplated in the policy-evaluation exercise.This problem can be addressed by making use of structural relations

that explicitly represent the dependence of economic decisions upon ex-pectations regarding future endogenous variables. The present study illus-trates how this can be done, deriving the structural relations that are to beused in the calculation of optimal policy rules from the first-order condi-tions (Euler equations) that characterize optimal private-sector behavior.These conditions explicitly involve private-sector expectations about the fu-ture evolution of endogenous variables, and often they only implicitly defineprivate-sector behavior, rather than giving a consumption equation or priceequation in closed form. My preference for this form of structural relationsis precisely that they are ones that should remain invariant (insofar as theproposed theory is correct) under changes in policy that alter the stochasticlaws of motion of the endogenous variables.Of course, the mere fact that the structural relations derived here follow

from explicit optimization problems for households and firms is no guaran-tee that they are correctly specified; the (fairly simple) optimization prob-lems that I consider here may or may not be empirically realistic. (Indeed,insofar as I illustrate the principles of my approach in the context of verysimple examples, one can be certain that they are not very precise repre-sentations of reality.) But this is not an objection to the method that I advo-cate here. It simply means that there is no substitute for careful empiricalresearch to flesh out the details of a quantitatively realistic account of themonetary transmission mechanism. While the present study does includesome discussion of the extent to which the simple models presented hereare consistent with empirical evidence, in order to motivate the introduc-tion of certain model elements, no attempt is made to set out a model that


is sufficiently realistic to be used for actual policy analysis in a central bank.Nonetheless, the basic elements of an optimizing model of the monetarytransmission mechanism, developed in Chapters 3 through 5, are ones thatI believe are representative of crucial elements of a realistic model; and in-deed, the illustrativemodels discussed here havemany elements in commonwith rational-expectationsmodels of themonetary transmissionmechanismthat are already being used for quantitative policy evaluation at a numberof central banks.A second advantage of proceeding from explicit microeconomic foun-

dations is that in this case, the welfare of private agents—as indicated bythe utility functions that underlie the structural relations of one’s modelof the transmission mechanism—provides a natural objective in terms ofwhich alternative policies should be evaluated. In taking this approach, thepresent study seeks to treat questions of monetary policy in a way that isalready standard in other branches of public economics, such as the analy-sis of optimal tax policy. Nonetheless, the approach is not common in theliterature on monetary policy evaluation, which instead typically evaluatesalternative policies in terms of ad hoc stabilization objectives for variousmacroeconomic indicators.Until recently, welfare-theoretic analyses ofmonetary policy have been as-

sociated exclusively with the problem of reducing the transactions frictions(sometimes called “shoe-leather costs”) that account for the use of moneyin purchases.5 This is because this was for a long time the only sort of in-efficiency present in general-equilibrium monetary models, which typicallyassumed perfectly flexible wages and prices and perfect competition. HereI show how welfare analysis of monetary policy is also possible in settingsthat incorporate nominal rigidities. Allowing for these additional frictions—crucial to understanding the real effects of alternative monetary policies—provides a welfare-theoretic justification for additional policy goals.As shown in Chapter 6, taking account of delays in the adjustment of

wages and prices provides a clear justification for an approach to monetarypolicy that aims at price stability. It might seem more obvious that allowingfor real effects of monetary policy provides a justification for concern withoutput stabilization. The stickiness of prices explains why actual output maydiffer from the natural rate, and so justifies a concern for the stabilizationof the “output gap,” that is, the discrepancy between the actual and naturallevels of output. But price stickiness also justifies a concern with price sta-bility. For when prices are not constantly adjusted, instability of the generallevel of prices creates discrepancies between relative prices owing to the ab-sence of perfect synchronization in the adjustment of the prices of different

5. For reviews of that traditional literature, see Woodford (1990) and Chari and Kehoe(1999).


goods. These relative-price distortions lead in turn to an inefficient sectoralallocation of resources, even when the aggregate level of output is correct.Moreover, the present theory implies not only that price stability should

matter in addition to stability of the output gap, but also that, at least undercertain circumstances, inflation stabilization eliminates any need for fur-ther concern with the level of real activity. This is because, at least under theconditions describedmore precisely in Chapter 6, the time-varying efficientlevel of output is the same (up to a constant, which does not affect the basicpoint) as the level of output that eliminates any incentive for firms on aver-age to either raise or lower their prices. It then follows that there is no con-flict between the goal of inflation stabilization and output-gap stabilization,once the welfare-relevant concept of the output gap is properly understood.Furthermore, because of the difficulty involved in measuring the efficientlevel of economic activity in real time—depending as this does on variationsin production costs, consumption needs, and investment opportunities—itmay well bemore convenient for a central bank to concern itself simply withmonitoring the stability of prices.The development of an explicit welfare analysis of the distortions result-

ing from inflation variations has advantages beyond the mere provision ofa justification for central bankers’ current concern with inflation stabiliza-tion. For the theory presented here also provides guidance as to which priceindex it is most desirable to stabilize. This is a question of no small practicalinterest. For example, the stock-market booms and crashes in many indus-trial nations in the late 1990s led to discussion of whether central banksought not target an inflation measure that took account of “asset-price in-flation” as well as goods prices.6

The answer provided by the theory developed here is no. The prices thatmonetary policy should aim to stabilize are the ones that are infrequentlyadjusted and that consequently can be expected to become misaligned inan environment that requires these prices tomove in either direction. Largemovements in frequently adjusted prices—and stock prices are among themost flexible—can instead be allowed without raising such concerns, and ifallowing them to move makes possible greater stability of the sticky prices,such instability of the flexible prices is desirable.7 In Chapter 6, I showhow such a conclusion can be justified from the point of view of welfare

6. For examples of scholarly attention to the question, see Goodhart (1999) and Bryan etal. (2002).7. The basic point was already evident to authors of the Stockholm school: “If one desires

the greatest possible diminution of the business cycle . . . then one must try to stabilize anindex of those prices which are sticky in themselves. . . . Stability of the level of the sticky pricespermits a certain freedom for all other price levels, including capital values. . . . It is evidentthat [the price of capital goods] is the last price that one should try to stabilize in a capitalistsociety. . . . The same is naturally true for all indices of flexible commodity prices” (Myrdal,


economics. I further show how to develop a quantitative measure of thedeadweight loss resulting from stabilization of alternative price indices, sothat more subtle distinctions between the relative stickiness of differentprices can be dealt with.In addition to implying that an appropriate inflation target ought not

involve asset prices, the present theory suggests that not all goods prices areequally relevant. Rather, central banks should target a measure of “core”inflation that places greater weight on those prices that are stickier. Fur-thermore, insofar as wages are also sticky, a desirable inflation target shouldtake account of wage inflation as well as goods prices. The empirical resultsdiscussed in Chapter 3 suggest that wages and prices are sticky to a similarextent, suggesting (as I show in Chapter 8) that a desirable inflation targetshould put roughly equal weight on wage and price inflation.

2 The Importance of Policy Commitment

Thus far, I have summarized a theoretical justification for the concern ofthe inflation-targeting central banks with price stability. But why shouldit follow that there is a need for public commitment to a target inflationrate, let alone for commitment to a systematic procedure for determiningappropriate instrument settings? Why is it not enough to appoint centralbankers with a sound understanding of the way the economy works andthen grant them complete discretion to pursue the public interest in the waythat they judge best? Should it not follow from my analysis that this wouldresult in price stability, to the extent that it is possible given the instrumentsavailable to the central bank and the information available at the time thatpolicy decisions must be made?I argue instead that there is good reason for a central bank to commit

itself to a systematic approach to policy that not only provides an explicitframework for decisionmaking within the bank, but that is also used to ex-plain the bank’s decisions to the public. There are two important advantagesof commitment to an appropriately chosen policy rule of this kind. One isthat the effectiveness of monetary policy depends as much on the public’sexpectations about future policy as upon the bank’s actual actions. Henceit is important not only that a bank manage to make the right decision asoften as possible, but that its actions be predictable.The second, and subtler, reason is that even if the public has no difficulty

in correctly perceiving the pattern in the central bank’s actions—as assumed

1931, pp. 192–193). Simons (1948) and Meade (1951) advocated targeting a domestic-goodsprice index rather than a consumer price index on similar grounds; the CPI would include theprices of imported goods, that could vary freely through exchange-rate movements. Claridaet al. (2001) also obtain the latter conclusion, in the context of a fully articulated open-economy sticky-price model.

2. The Importance of Policy Commitment 15

under the hypothesis of rational expectations—if a bank acts at each dateunder the assumption that it cannot commit itself to any future behavior(and is not bound by any past commitments), it will choose a systematicpattern of behavior that is suboptimal. I take up each of these argumentsin turn.

2.1 Central Banking as Management of Expectations

The first advantage of commitment to a policy rule is that it facilitates publicunderstanding of policy. It is important for the public to understand thecentral bank’s actions, to the greatest extent possible, not only for reasonsof democratic legitimacy—though this is an excellent reason itself, giventhat central bankers are granted substantial autonomy in the execution oftheir task—but also in order for monetary policy to be most effective.For successful monetary policy is not so much a matter of effective con-

trol of overnight interest rates as it is of shaping market expectations of theway in which interest rates, inflation, and income are likely to evolve over thecoming year and later. On the one hand, optimizing models imply that pri-vate sector behavior should be forward looking; hence expectations aboutfuture market conditions should be important determinants of current be-havior. It follows that, insofar as it is possible for the central bank to af-fect expectations, this should be an important tool of stabilization policy.Moreover, given the increasing sophistication of market participants aboutcentral banking over the past two decades, it is plausible to suppose thata central bank’s commitment to a systematic policy will be factored intoprivate-sector forecasts—at least insofar as the bank’s actions are observedto match its professed commitments.Not only do expectations about policy matter, but, at least under current

conditions, very little else matters. Few central banks of major industrial na-tions still makemuch use of credit controls or other attempts to directly reg-ulate the flow of funds through financial markets and institutions. Increasesin the sophistication of the financial system have made it more difficult forsuch controls to be effective, and in any event the goal of improvementof the efficiency of the sectoral allocation of resources stressed previouslywould hardly be served by such controls, which (if successful) inevitablycreate inefficient distortions in the relative cost of funds to different partsof the economy.Instead, banks restrict themselves to interventions that seek to control

the overnight interest rate in an interbankmarket for central-bank balances(e.g., the federal funds rate in the United States). But the current level ofovernight interest rates as such is of negligible importance for economicdecisionmaking. If a change in the overnight rate were thought to implyonly a change in the cost of overnight borrowing for that one night, theneven a large change (say, a full percentage point increase) would make little


difference to anyone’s spending decisions. The effectiveness of changes incentral-bank targets for overnight rates in affecting spending decisions (andhence ultimately pricing and employment decisions) is wholly dependentupon the impact of such actions upon other financial-market prices, suchas longer-term interest rates, equity prices, and exchange rates. These areplausibly linked, through arbitrage relations, to the short-term interest ratesmost directly affected by central-bank actions. But it is the expected futurepath of short-term rates over coming months and even years that shouldmatter for the determination of these other asset prices, rather than thecurrent level of short-term rates by itself.8

Thus the ability of central banks to influence expenditure, and hencepricing, decisions is critically dependent upon their ability to influencemar-ket expectations regarding the future path of overnight interest rates, andnot merely their current level. Better information on the part of marketparticipants about central-bank actions and intentions should increase thedegree to which central-bank policy decisions can actually affect these ex-pectations and so increase the effectiveness of monetary stabilization policy.Insofar as the significance of current developments for future policy is clearto the private sector, markets can to a large extent “do the central bank’swork for it,” in that the actual changes in overnight rates required to achievethe desired changes in incentives can bemuchmoremodest when expectedfuture rates move as well.9

An obvious consequence of the importance of managing expectations isthat a transparent central-bank decisionmaking process is highly desirable.This has come to be widely accepted by central bankers over the past decade.(See Blinder et al., 2001, for a detailed and authoritative discussion.) Butit is sometimes supposed that the most crucial issues are ones such as thefrequency of press releases or the promptness and detail with which the

8. An effect of the same kind is obtained in the basic “neo-Wicksellian” model developedin Chapter 4, insofar as the short-run real rate of interest determines not the absolute level ofdesired private-sector expenditure, but rather the current level relative to the expected futurelevel of expenditure, as a result of an Euler equation for the optimal timing of expenditure.Expected future expenditure, relative to expected expenditure even farther in the future,similarly depends upon expected future short rates, and so on for expectations regarding thestill farther future.9. There is evidence that this is already happening, as a result both of greater sophistication

on the part of financial markets and greater transparency on the part of central banks, the twodeveloping in a sort of symbiosis with one another. Blinder et al. (2001, p. 8) argue that in theperiod from early 1996 through the middle of 1999, one could observe the U.S. bond marketmoving in response to macroeconomic developments that helped to stabilize the economy,despite relatively little change in the level of the federal funds rate, and suggest that thisreflected an improvement in the bond market’s ability to forecast Fed actions before theyoccur. Statistical evidence of increased forecastability of Fed policy by the markets is providedby Lange et al. (2001), who show that the ability of Treasury bill yields to predict changes inthe federal funds rate some months in advance has increased since the late 1980s.


minutes of policy deliberations are published. Instead, from the perspectivesuggested here, what is important is not so much that the central bank’sdeliberations themselves be public, as that the bank give clear signals aboutwhat the public should expect it to do in the future. The public needs tohave as clear as possible an understanding of the rule that the central bankfollows in deciding what it does. Inevitably, the best way to communicateabout this is by offering the public an explanation of the decisions thathave already been made; the bank itself would probably not be able todescribe how it might act in all conceivable circumstances, most of whichwill never arise.Some good practical examples of communication with the public about

the central bank’s policy commitments are provided by the Inflation Reportsof the leading inflation-targeting banks. These reports do not pretend togive a blow-by-blow account of the deliberations by which the central bankreached the position that it has determined to announce, but they do ex-plain the analysis that justifies the position that has been reached. This anal-ysis provides information about the bank’s systematic approach to policy byillustrating its application to the concrete circumstances that have arisensince the last report; and it provides information about how conditions arelikely to develop in the future through explicit discussion of the bank’s ownprojections. Because the analysis is made public, it can be expected to shapefuture deliberations, with the bank knowing that it should be expected toexplain why views expressed in the past are not being followed later. Thusa commitment to transparency of this sort helps to make policy more fullyrule based and also increases the public’s understanding of the rule.It is perhaps worth clarifying further what I intend by “rule-based” pol-

icy. I do not mean that a bank should commit itself to an explicit state-contingent plan for the entire foreseeable future, specifying what it woulddo under every circumstance thatmight possibly arise. That would obviouslybe impractical, even under complete unanimity about the correct model ofthe economy and the objectives of policy, simply because of the vast num-ber of possible futures. But it is also not necessary. To obtain the benefitsof commitment to a systematic policy, it suffices that a central bank commititself to a systematic way of determining an appropriate response to futuredevelopments, without having to list all of the implications of the rule forpossible future developments.10

Nor is it necessary to imagine that commitment to a systematic rulemeans that once a rule is adopted it must be followed forever, regard-

10. I show in Chapter 8 how policy rules can be designed that can be specified without anyreference to particular economic disturbances, but that nonetheless imply an optimal equilib-rium response to additive disturbances of an arbitrary type. The targeting rules advocated bySvensson (1999, 2003b) are examples of rules of this kind.


less of subsequent improvements in understanding the effects of mone-tary policy on the economy, including experience with the consequencesof implementing the rule. If the private sector is forward looking, and it ispossible for the central bank to make the private sector aware of its policycommitments, then there are important advantages of commitment to a pol-icy other than discretionary optimization—that is, simply doing what seemsbest at each point in time, with no commitment regarding what may bedone later. This is because there are advantages to having the private sectorable to anticipate delayed responses to a disturbance that may not be optimalex post if one reoptimizes taking the private sector’s past reaction as given.But one can create the desired anticipations of subsequent behavior—andjustify them—without committing to following a fixed rule in the future nomatter what may happen in the meantime.It is enough that the private sector have no grounds to forecast that the

bank’s behavior will be systematically different from the rule that it pretendsto follow. This will be the case if the bank is committed to choosing a ruleof conduct that is justifiable on certain principles, given its model of theeconomy. (An example of the sort of principles that I have in mind is givenin Chapter 8.) The bank can then properly be expected to continue tofollow its current rule, as long as its understanding of the economy doesnot change. Furthermore, as long as there is no predictable direction inwhich its future model of the economy should be different from its currentone, private-sector expectations should not be different from those in thecase of an indefinite commitment to the current rule. Yet changing to abetter rule remains possible in the case of improved knowledge (which isinevitable); and insofar as the change is justified in terms of both establishedprinciples and a change in the bank’s model of the economy that can itselfbe defended, this need not impair the credibility of the bank’s professedcommitments.It follows that rule-based policymaking necessarily means a decision pro-

cess in which an explicit model of the economy (albeit one augmented byjudgmental elements) plays a central role, both in the deliberations of thepolicy committee and in explanation of those deliberations to the public.This too has been a prominent feature of recent innovations in the conductof monetary policy by the inflation-targeting central banks. While there isundoubtedly much room for improvement in both current models and cur-rent approaches to the use of models in policy deliberations, one can onlyexpect the importance of models to policy deliberations to increase in aworld of increasingly sophisticated financial markets.

2.2 Pitfalls of Conventional Optimal Control

It is not enough that a central bank have sound objectives (reflecting a cor-rect analysis of social welfare), that it make policy in a systematic way, using


a correct model of the economy and a staff that is well trained in numeri-cal optimization, and that all this be explained thoroughly to the public. Abank that approaches its problem as one of optimization under discretion—deciding afresh on the best action in each decision cycle, with no commit-ment regarding future actions except that they will be the ones that seembest in whatever circumstances may arise—may obtain a substantially worseoutcome, from the point of view of its own objectives, than one that com-mits itself to follow a properly chosen policy rule. As Kydland and Prescott(1977) first showed, this can occur even when the central bank has a correctquantitative model of the policy trade-offs that it faces at each point in timeand the private sector has correct expectations about the way that policy willbe conducted.At first thought, discretionary optimization might seem exactly what one

would want an enlightened central bank to do. All sorts of unexpectedevents constantly occur that affect the determination of inflation and realactivity, and it is not hard to see that, in general, the optimal level of interestrates at any point in time should depend on precisely what has occurred. Itis plainly easiest, as a practical matter, to arrange for such complex statedependence of policy by having the instrument setting at a given point intime be determined only after the unexpected shocks have already beenobserved. Furthermore, it might seem that the dynamic programming ap-proach to the solution of intertemporal optimization problems provides jus-tification for an approach in which a planning problem is reduced to a seriesof independent choices at each of a succession of decision dates.But standard dynamic programming methods are valid only for the opti-

mal control of a system that evolves mechanically in response to the currentaction of the controller, as in the kind of industrial problems of typical in-terest in engineering control theory. The problem ofmonetary stabilizationpolicy is of a different sort, in that the consequences of the central bank’sactions depend not only upon the sequence of instrument settings up untilthe present time, but also upon private-sector expectations regarding fu-ture policy. In such a case, sequential (discretionary) optimization leads toa suboptimal outcome because at each decision point, prior expectationsare taken as given, rather than as something that can be affected by pol-icy. Nonetheless, the predictable character of the central bank’s decisions,taken from this point of view, does determine the (endogenous) expecta-tions of the private sector at earlier dates, under the hypothesis of rationalexpectations. A commitment to behave differently that is made credible tothe private sector could shape those expectations in a different way, andbecause expectations matter for the determination of the variables that thecentral bank cares about, in general outcomes can be improved throughshrewd use of this opportunity.The best-known example of a distortion created by discretionary opti-

mization is the “inflation bias” analyzed by Kydland and Prescott (1977)


and Barro and Gordon (1983). In the presence of a short-run Phillips-curvetrade-off between inflation and real activity (given inflation expectations)and a target level of real activity higher than the one associated with anoptimal inflation rate (in the case of inflation expectations also consistentwith that optimal rate), these authors showed that discretionary optimiza-tion leads to a rate of inflation that is inefficiently high on average, owing toneglect of the way that pursuit of such a policy raises inflation expectations(causing an adverse shift of the short-run Phillips curve). A variety of solu-tions to the problem of inflation bias have been proposed. One influentialidea is that this bias can be eliminated by assigning the central bank targetsfor inflation and output that differ from those reflected in the true socialwelfare function (i.e., the central-bank objective assumed by Kydland andPrescott or Barro and Gordon), without otherwise constraining the centralbank’s discretion in the selection of policies to achieve its objective. This isone of the primary reasons for the popularity of inflation targeting, whichinvolves commitment of a central bank to the pursuit of an assigned targetrather than being left to simply act as seems best for society at any point intime, while leaving the bank a great deal of flexibility as to the way in whichthe assigned goal is to be pursued.However, the distortions resulting from discretionary optimization go be-

yond simple bias in the average levels of inflation or other endogenous vari-ables; this approach to the conduct of policy generally results in suboptimalresponses to shocks as well, as shown in Chapter 7. For example, varioustypes of real disturbances can create temporary fluctuations in what Wick-sell called the “natural rate of interest,” meaning (as shown in Chapter 4)that the level of nominal interest rates required to stabilize both inflationand the output gap varies over time. However, the amplitude of the adjust-ment of short-term interest rates can be more moderate—and still have thedesired size of effect on spending and hence on both output and inflation—if it is made more persistent, so that when interest rates are increased, theywill not be expected to quickly return to their normal level, even if the realdisturbance that originally justified the adjustment has dissipated. Becauseaggregate demand depends upon expected future short rates as well as oncurrent short rates, amore persistent increase of smaller amplitude can havean equal affect on spending. If one also cares about reducing the volatilityof short-term interest rates, a more inertial interest-rate policy of this kindis preferable; that is, the anticipation that the central bank will follow such apolicy leads to a preferable rational-expectations equilibrium. But a centralbank that optimizes under discretion has no incentive to continue to main-tain interest rates high once the initial shock has dissipated. At that point,prior demand has already responded to whatever interest-rate expectationswere held then, and the bank has no reason to take into account any effectupon demand at an earlier date in setting its current interest-rate target.


This distortion in the dynamic response of interest-rate policy to distur-bances cannot be cured by any adjustment of the targets that the bank isdirected to aim for regardless of what disturbances may occur. Rather, pol-icy must be made history dependent, that is, dependent upon past conditionseven when they are no longer relevant to the determination of the currentand future evolution of the variables that the bank cares about. Indeed, ingeneral no purely forward-looking decision procedure—one that makes thebank’s action at each decision point a function solely of the set of possiblepaths for its target variables from that time onward—can bring about op-timal equilibrium responses to disturbances. Discretionary optimization isan example of such a procedure, and it continues to be when the bank’sobjective is modified, if the modification does not introduce any historydependence. But other popular proposals are often purely forward lookingas well. Thus the classic “Taylor rule” (Taylor, 1993) prescribes setting aninterest-rate operating target at each decision point as a function of cur-rent estimates of inflation and the output gap only (see below), and Taylor(1999b) expresses skepticism about the desirability of partial-adjustment dy-namics of the kind that characterize most estimated central-bank reactionfunctions. Popular descriptions of inflation-forecast targeting are typicallypurely forward looking as well. The interest-rate setting at each decisionpoint is to be determined purely as a function of the forecast from that dateforward for inflation (and possibly other target variables). Thus the intu-ition that optimal policy should be purely forward looking seems to be fairlycommonplace; but when the private sector is forward looking, any purelyforward-looking criterion for policy is almost invariably suboptimal.Obtaining a more desirable pattern of responses to random disturbances

therefore requires commitment to a systematic policy rule, and not justa (one-time) adjustment of the bank’s targets. The primary task of thisstudy is to provide principles that can be used in the design of such rules.By saying that a policy rule is necessary, I mean to draw a distinction withtwo other conceptions of optimal policy. One is discretionary optimization,as just discussed; specifying a rule means a more detailed description ofthe way in which a decision is to be reached than is involved in a simplecommitment to a particular objective. But I also mean to distinguish theapproach advocated here from the usual understanding of what an optimalcommitment involves.In the literature that contrasts policy commitment with discretionary

policymaking, following Kydland and Prescott, “commitment” is generallytaken to mean a specification, once and for all, of the state-contingentaction to be taken at each subsequent date. An optimal commitment isthen a choice of such a state-contingent plan so as to maximize the ex anteexpected value of the policymaker’s objective, as evaluated at the initial datet 0 at which the commitment is chosen. This leads to a description of optimal


policy in terms of a specification of the instrument setting as a function ofthe history of exogenous shocks since date t 0.But the solution to such an optimization problem is not an appealing pol-

icy recommendation in practice. For it is generally not time consistent : Solvingthe same optimization problem at a later date t1 to determine the optimalcommitment from that date onward does not result in a state-contingentplan from date t1 onward that continues the plan judged to be optimal atdate t 0. This is because the commitment chosen at date t 0 takes accountof the consequences of the commitments made for dates t1 and later forexpectations between dates t 0 and t1, while at date t1 these expectationsare taken as historical facts that cannot be changed by the policy chosenfrom then on. (This is just the reason why discretionary optimization doesnot lead to the same policy as an optimal commitment.) Hence this policyproposal cannot be regarded as proposing a decision procedure that canbe used at each date to determine the best action at that date. Rather, astate-contingent plan must be determined once and for all, for the rest oftime, and thereafter simply implemented, whether it continues to appeardesirable or not.Such a proposal is not a practical one for two reasons. First, enumera-

tion in advance of all of the possible subsequent histories of shocks is notfeasible—the kinds of situations that the central bank may face at a givendate are too various to possibly be listed in advance. Second, the arbitrari-ness of continuing to stick to a particular specified policy simply because itlooked good at a particular past date—the date t 0 at which one happened tomake the commitment—is sufficiently unappealing that one cannot imag-ine a central bank binding itself to behave in that way or the private sec-tor believing that it had. Here my argument is not that central bankers areincapable of commitment to a systematic rule of conduct, so that they areinevitably discretionary optimizers; it is rather that their commitment mustbe based upon an understanding of the rational justification of the rule,and not on the mere fact that it happens to have been chosen (even bythemselves) on a past occasion.Both problems can be avoided by commitment to a systematic rule for

determining their policy action at each decision point that does not reduceto a once-and-for-all specification of the instrument setting as a function ofthe history of shocks. In Chapter 8, it is shown that one can design rules forsetting the central bank’s interest-rate operating target that lead to optimaldynamic responses to shocks, without the rule specification having to referto the various disturbances that may have occurred. The disturbances affectthe instrument setting, of course. But they affect it either as a result of havinginfluenced endogenous variables, such as inflation and output, to which theinstrument setting responds or as a result of being factored into the centralbank’s projections of the future evolution of the economy under alternative


possible instrument settings. Such a rule can result in optimal equilibriumresponses to disturbances of any of a vast number of possible types, so thatthe potential disturbances need not even be listed in advance in order todescribe the rule and evaluate its desirability.The optimal rules derived in accordance with the principles set out in

Chapter 8 are also time invariant in form. This means that the optimal rulethat would be derived at date t 0, on the basis of a particular structural modelof themonetary transmissionmechanism and a particular understanding ofthe central bank’s stabilization objectives, is also derived at date t1, assumingthat the bank’s model and objectives remain the same. A commitment toconduct policy in accordance with a rule that is judged optimal by thiscriterion is thus time consistent, in the sense that reconsideration of thematter at a later date on the basis of the same principle leads to a decisionto continue the same course of action as had been intended earlier.11

Because of this, adherence to a policy rule need not be taken to meanadoption of a rule at some initial date, after which the rule is followedblindly, without ever again considering its desirability. Instead, rule-based pol-icymaking as the term is intended here means that at each decision point anaction is taken that conforms to a policy rule, which rule is itself one thatis judged to be optimal (from a “timeless perspective” that is explained inChapter 7) given the central bank’s understanding of the monetary trans-mission mechanism at the time that the decision is made. The desire to follow arule (and so to avoid the trap of discretionary optimization) does not meanthat the bank must refrain from asking itself whether adherence to the ruleis consistent with its stabilization objectives. It simply means that wheneverthis question is taken up, the bank should consider what an optimal rule ofconduct would be, rather than asking what an optimal action is on the in-dividual occasion, and that it should consider the desirability of alternativerules from an impartial perspective that does not amount to simply find-ing a rationalization for the action it would like to take on this particularoccasion.12 A central bank might reconsider this question as often as it likes,

11. Note that “time consistency” in the sense that I use the term here does not mean thatthe policymaker does not believe at any time that it is possible to achieve a higher expectedvalue for its objective by deviating from its intended rule. Time consistency does not requirethis, because this is not the criterion according to which the central bank’s action is judged tobe optimal at any time, including the initial date t 0.12. The distinction between these two perspectives is similar to the distinction that is made

in ethical theory between “rule utilitarianism” and “act utilitarianism” (Brandt, 1959; Harsanyi,1982). Act utilitarianism is the view that the right act on any occasion is the one that willmaximize social utility in the situation that the actor is in at that time. Rule utilitarianisminstead maintains that a right act is one that conforms to the correct rule for this sort ofsituation, where a correct rule is one that would maximize social utility if always followed inall situations of this type.


without being led into the kind of suboptimal behavior that results fromdiscretionary optimization. Moreover, when considering the desirability ofa policy rule, it is correct for the bank to consider the effects of its being ex-pected to follow the rule indefinitely, even though it does not contemplatebinding itself to do so; for as long as its view of the policy problem doesnot change (which it has no reason to expect), a commitment to rule-basedpolicymaking should guarantee that it will continue to act according to therule judged to be optimal.Rule-based policymaking in this sense avoids the sorts of rigidity that are

often associated with commitment to a “rule” and that probably account formuch of the resistance that central bankers often display toward the con-cept of a policy rule. A commitment to rule-based policymaking does notpreclude taking account of all of the information, from whatever sources,that the central bank may have about current economic conditions, includ-ing the recognition that disturbances may have occurred that would nothave been thought possible a few months earlier. For a policy rule need notspecify the instrument setting as a function of a specified list of exogenousstates, and indeed it is argued in Chapter 7 that an optimal rule should ingeneral not take this form. Nor does it preclude changing the form of thepolicy rule when the bank’s view of the monetary transmission changes, asit surely will, owing both to institutional change in economies themselvesand to the progress of knowledge in economics. Hence it allows the sortof flexibility that is often associated with the term “discretion,” while at thesame time eliminating the systematic biases that follow from policy analysisthat naively applies dynamic-programming principles.

3 Monetary Policy without Control of a Monetary Aggregate

Thus far I have discussed the desirability of a monetary policy rule withoutsaying much about the precise form of rule that is intended. To be moreconcrete, the present study considers the design of a rule to be used indetermining a central bank’s operating target for a short-term nominal in-terest rate. This target will ordinarily be revised at intervals of perhaps oncea month (as at the ECB) or eight times a year (as in the United States).13

My focus on the choice of an interest-rate rule should not surprise readersfamiliar with the current practice of central banks. Monetary policy deci-sionmaking almost everywhere means a decision about the operating tar-get for an overnight interest rate, and the increased transparency aboutpolicy in recent years has almost always meant greater explicitness about

13. The question of the optimal frequency of reconsideration of the interest-rate target isone of obvious practical interest. But I shall not take it up in this study, as I consider optimalpolicy in the context of a discrete-time model of the transmission mechanism with “periods”corresponding to the length of the central bank’s decision cycle.

3. Monetary Policy without Control of a Monetary Aggregate 25

the central bank’s interest-rate target and the way in which its interest-ratedecisions are made. In such a context, it is natural that adoption of a policyrule should mean commitment to a specific procedure for deciding whatinterest-rate target is appropriate.Nonetheless, theoretical analyses of monetary policy have until recently

almost invariably characterized policy in terms of a path for the moneysupply, and discussions of policy rules in the theoretical literature havemainly considered money-growth rules of one type or another. This curiousdisjunction between theory and practice predates the enthusiasm of the1970s for monetary targets. Goodhart (1989) complains of “an unhelpfuldichotomy, between the theory and the reality of Central Bank operations,”which equally characterized the work of John Maynard Keynes and MiltonFriedman:

When either of these two great economists would discuss practical pol-icy matters concerning the level of short-term interest rates, they had nodoubts that these were normally determined by the authorities, and couldbe changed by them, and were not freely determined in the market. . . . Butwhen they came to their more theoretical papers, they often reverted to theassumption that the Central Bank sets the nominal money stock, or alterna-tively fixes the level of the monetary base, [with] the demand and supply ofmoney . . . equilibrated in the short run . . . by market-led developments innominal interest rates. (pp. 330–331)

The present study seeks to revive the earlier approach of Knut Wickselland considers the advantages of systematic monetary policies that are de-scribed in terms of rules for setting a nominal interest rate. While the im-plied evolution of the money supply is sometimes discussed, the questionis often ignored. Some of the time, I do not bother to specify policy (or aneconomicmodel) in sufficient detail to determine the associated path of themoney supply, or even to tell if one can be uniquely determined in principle.Some readers may fear as a result that I consider an ill-posed question—thatthe “policy rules” studied here may not represent sufficiently complete de-scriptions of a policy to allow its consequences to be determined or maynot represent states of affairs that the central bank is able to bring about.Hence some general remarks may be appropriate about why it is possibleto conceive of the problem of monetary policy as a problem of interest-ratepolicy before turning to examples of the specific types of interest-rate rulesthat I wish to consider.

3.1 Implementing Interest-Rate Policy

An argument that is sometimes advanced for specifying monetary policy interms of a rule for base-money growth rather than an interest-rate rule isthat central banks do not actually fix overnight interest rates. Even when


banks have an operating target for the overnight rate, they typically seekto implement it through open-market operations in Treasury securities ortheir equivalent—that is, by adjusting the supply of central-bank liabilities toa level that is expected to cause the market for overnight cash to clear nearthe target rate. Thus it may be argued that the action that the central bankactually takes each day is an adjustment of the nominal magnitude of themonetary base, so that a complete specification of policy should describethe size of this daily adjustment.But even when banks implement their interest-rate targets entirely

through quantity adjustments, as is largely correct as a description of cur-rent U.S. arrangements, this conclusion hardly follows. Central banks likethe U.S. Federal Reserve determine their quantity adjustments through atwo-step procedure: first the interest-rate target is determined by a mone-tary policy committee (the Federal Open Market Committee in the UnitedStates) without consideration of the size of the implied open-market oper-ations, and then the appropriate daily open-market operations required tomaintain the funds rate near the target are determined by people closerto the financial markets (mainly the Trading Desk at the New York Fed).The higher-level policy decision about the interest-rate target is the morecomplicated one, made much less frequently because of the complexity ofthe deliberations involved,14 and it is accordingly this decision with whichthe present study is concerned.Nor is it the case that a central bank’s interest-rate target must be im-

plemented through choice of an appropriate supply of central-bank liabili-ties. A central bank can also influence the interest rate at which banks lendovernight cash to one another through adjustment of the interest rate paidon overnight balances held at the central bank and/or the interest rate atwhich the central bank is willing to lend overnight cash to banks that runoverdrafts on their clearing accounts at the central bank. These are impor-tant policy tools outside the United States, and in some countries are theprimary means through which the central bank implements its interest-ratetargets.As is discussed in more detail in Woodford (2001c), countries like Can-

ada, Australia, and New Zealand now implement monetary policy througha “channel system.” In a system of this kind, the overnight interest rate iskept near the central bank’s target rate through the provision of standing

14. The comparative simplicity of the decision about each day’s open-market operation isnot so much because each day’s demand for Fed balances is highly predictable as because theFed learns immediately how much it has misjudged market demand each day and can act thefollowing day in response to the previous day’s gap between the actual funds rate and the targetrate. Owing to intertemporal substitution in the demand for reserves under U.S. regulations,a credible commitment by the Fed to respond the following day is enough to keep the fundsrate from deviating too much from the target most of the time. See Taylor (2001) for furtherdiscussion of the Trading Desk’s reaction function.


facilities by the central bank, with interest rates determined by the centralbank’s current target interest rate ı̄ t . In addition to supplying a certain ag-gregate quantity of clearing balances (adjusted through open-market oper-ations), the central bank offers a lending facility through which it standsready to supply an arbitrary amount of additional overnight balances atan interest rate determined by a fixed spread over the target rate (i.e.,i lt = ı̄ t + δ). In the countries just mentioned, the spread δ is generally equalto 25 basis points, regardless of the level of the target rate. Finally, deposi-tory institutions that settle payments through the central bank also have theright to maintain excess clearing balances overnight with the central bankat a deposit rate idt = ı̄ t − δ, where δ is the same fixed spread.The lending rate, on the one hand, and the deposit rate, on the other,

then define a channel within which overnight interest rates should be con-tained.15 Because these are both standing facilities (unlike the Fed’s dis-count window in the United States), no bank has any reason to pay anotherbank a higher rate for overnight cash than the rate at which it could borrowfrom the central bank. Similarly, no bank has any reason to lend overnightcash at a rate lower than the rate at which it can deposit with the centralbank. The result is that the central bank can control overnight interest rateswithin a fairly tight range regardless of what the aggregate supply of clearingbalances might be; frequent quantity adjustments accordingly become lessimportant.Woodford (2001c) describes a simple model of overnight interest-rate

determination under such a system. In this model, the daily demand forclearing balances by depository institutions depends only on the locationof the interbank market rate relative to the channel established by the twostanding facilities, rather than on the absolute level of this interest rate. Theinterbank market then clears at an interest rate

it = idt + F (−St/σt )(i lt − idt

), (3.1)

where St is the aggregate supply of clearing balances (determined by thecentral bank’s open-market operations), σt is a factor measuring the degreeof uncertainty about payment flows on a given day, and F is a cumulativedistribution function that increases monotonically from 0 (when its argu-ment is −∞) to 1 (as the argument approaches +∞).

15. It is arguable that the actual lower bound is somewhat above the deposit rate because ofthe convenience and lack of credit risk associated with the deposit facility, and similarly that theactual upper bound is slightly above the lending rate because of the collateral requirementsand possible stigma associated with the lending facility. Nonetheless, market rates are observedto stay within the channel established by these rates (except for occasional slight breaches ofthe upper bound during the early months of operation of Canada’s system—see Figure 1.1),and typically near its center.


As noted, the market overnight rate is necessarily within the channel:idt ≤ it ≤ i lt . Its exact position within the channel should be a decreasingfunction of the supply of central-bank balances. The model predicts anequilibrium overnight rate at exactly the target rate (the midpoint of thechannel) when the supply of clearing balances is equal to

St = −F−1(1/2) σt . (3.2)

If the probability distribution of unexpected payment flows faced by eachinstitution is roughly symmetric, so that F (0) is near one-half, then theaggregate supply of clearing balances required to maintain the overnightrate near the target rate should not varymuchwith changes in σt .Even if thisis not quite true, the adjustments of the supply of clearing balances requiredby (3.2) are unrelated to changes in the target level of interest rates.Thus achievement of the central bank’s operating target does not require

any quantity adjustments through open-market operations in response todeviations of themarket rate from the target rate; nor are any changes in thesupply of central-bank balances required when the bank wishes to changethe level of overnight interest rates. The target level of clearing balances inthe system (3.2) has to be adjusted only in response to “technical” factors(e.g., changes in the volume of payments on certain days that can be ex-pected to affect the σi), but not on occasions when it is desired to “tighten”or “loosen”monetary policy. Instead, changes in the level of overnight rates,when desired, are brought about through the shifts in the deposit rate andlending rate that automatically follow from a change in the target rate (andconstitute the operational meaning of such a change), without any need forquantity adjustments.This type of system has proven highly effective in Canada, Australia, and

New Zealand in controlling the level of overnight interest rates. For exam-ple, Figure 1.1 plots the overnight rate in Canada since the adoption of theLarge-Value Transfer System for payments in February 1999, at which timethe standing facilities described previously were adopted.16 One observesthat the channel system has been quite effective, at least since early in 2000,in keeping the overnight interest rate not only within the Bank’s 50-basis-point operating band or channel, but usually within about 1 basis pointof the target rate. Australia and New Zealand similarly now achieve con-siderably tighter control of overnight interest rates than is realized underthe current operating procedures employed in the United States.17 Forpurposes of comparison, Figure 1.2 plots the federal funds rate together

16. A system of the kind described here has been used in Australia since June 1998, andin New Zealand since March 1999.17. See Woodford (2001c) for corresponding plots for the other two countries, and for

discussion of the differences in the four countries’ ability to respond to the Y2K panic withoutloss of control of short-term interest rates.


Feb99 Aug99 Feb00 Aug00 Feb01 Aug01 Feb02 Aug02 Feb03

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

overnight rate

target

channel

Figure 1.1 The channel or operating band and the market overnight rate since intro-duction of the LVTS system in Canada. Source: Bank of Canada.

with the Fed’s operating target over the same time period. Note that thestandard deviation of the gap between the target and actual federal fundsrate is much larger in the United States than in the countries using channelsystems (about 1 basis point for Canada, but over 10 basis points for theUnited States), even under normal circumstances. At times of particularuncertainty about money demand (the Y2K panic, the 9/11/01 attacks onthe United States), the deviations from the target funds rate in the UnitedStates have been much larger, whereas the same events had little effect onovernight rates in countries like Canada.Thus the quantity adjustments of the supply of central-bank balances18

that are involved in implementation of interest-rate policy are quite different

18. I refer here to adjustments of the supply of central-bank balances rather than adjust-ments of the monetary base because in all of the countries under discussion, changes in thepublic’s demand for currency are automatically accommodated by open-market operationsthat change the monetary base while seeking to insulate the supply of central-bank balancesfrom the effects of such developments. Thus despite the emphasis of the academic literatureon monetary-base rules, in practice a quantity-targeting rule that is intended to directly specifythe central bank’s daily open-market operation would have to specify a target supply of central-bank balances rather than a target value for the monetary base.


Jan99 Jul99 Jan00 Jul00 Jan01 Jul01 Jan02 Jul02 Jan03

1

2

3

4

5

6

7 federal funds ratetarget

Figure 1.2 The U.S. federal-funds rate and the Fed’s operating target. Source: FederalReserve Board.

under a channel system as opposed to the system used in the United States.In the latter, policy can be tightened only by restricting the supply of Fedbalances, so that the equilibrium spread between the return available oninterbank lending and that available on Fed balances increases; in Canada,on the other hand, there need be no change in supply, as there is no desireto change the spreads i lt − it or it − idt . Yet there is no reason to believethat these institutional details have any important consequences for theeffects of interest-rate policy on these economies, and hence for the wayin which it makes sense for these different central banks to determine theirinterest-rate operating targets. It follows that these conclusions would beof less universal validity if I were to formulate them in terms of a rulefor determining the appropriate size of open-market operations, assumingAmerican institutional arrangements.Furthermore, for a country with a channel system, it would not be pos-

sible to formulate this advice in terms of a quantity-targeting rule. On theoccasions upon which it is appropriate for the central bank to tighten orloosen policy, this does not imply any change in the appropriate target for


the supply of central-bank balances; yet this does not at all mean that thecentral bank should not act! Because the crucial policy instruments in thesecountries are in fact the interest rates associated with the two standing fa-cilities, which are in turn directly based on the time-varying interest-ratetarget, a policy rule for such countries must necessarily be formulated as aninterest-rate rule. In fact, this way of specifying monetary policy is equallyconvenient for a country like the United States, and is the one that I use inthis study.

3.2 Monetary Policy in a Cashless Economy

Another case in which amonetary policy prescription would have to be spec-ified in terms of an interest-rate rule would be if the foregoing advice wereto be applicable to a “cashless” economy, by which I mean an economy inwhich there are no monetary frictions whatsoever. In a hypothetical economyof this kind, central-bank liabilities have no special role to play in the pay-ments system that results in a willingness to hold them despite the fact thatthey yield a lower return than other, equally riskless short-term claims. Con-sideration of this extreme case is of interest for two reasons.First, it is possible to imagine that in the coming century the development

of electronic payments systems could not only substitute for the use of cur-rency in transactions, but also eliminate any advantage of clearing paymentsthrough accounts held at the central bank, as discussed by King (1999). Thisprospect is highly speculative at present; most current proposals for variantsof “electronic money” still depend upon the final settlement of transactionsthrough the central bank, even if payments are made using electronic sig-nals rather than old-fashioned instruments such as paper checks.19 Yet itis possible that in the future central banks will face the problem of whattheir role should be in such a world. Moreover, the question of how thedevelopment of electronic money should be regulated will face them muchsooner. If one takes the view that monetary policy can be implemented onlyby rationing the supply of something that fulfills an essential function inthe payments system, it is likely to be judged important to prevent the devel-opment of alternatives to payments using central-bank money in order tohead off a future in which the central bank is unable to do anything at all onbehalf of macroeconomic stabilization—in which it becomes “an army withonly a signal corps,” in the evocative phrase of Benjamin Friedman (1999).

19. Charles Freedman (2000), for one, argues that the special role of central banks inproviding for final settlement is unlikely ever to be replaced, owing to the unimpeachablesolvency of these institutions, as government entities that can create money at will. Some, suchas Goodhart (2000), equally doubt that electronic media can ever fully substitute for the useof currency.


A second reason why it is useful to consider policy implementation in thishypothetical case is that if I can show that effective interest-rate control ispossible even in the complete absence of monetary frictions, it may well sim-plify the analysis basic issues in the theory of monetary policy to start fromthe frictionless case, just as a physicist does when analyzing the motion ofa pendulum or the trajectory of a cannonball. The appeal of this analyticalapproach was clear already toWicksell (1898), who famously began his anal-ysis (though writing at the end of the nineteenth century!) by consideringthe case of a “pure credit economy,” defined as

A state of affairs in which money does not actually circulate at all, neither inthe form of coin (except perhaps as small change) nor in the form of notes,but where all domestic payments are effected by means of . . . bookkeepingtransfers. (p. 70)

This is the approach that is taken in the chapters to follow. The basic model(developed beginning in Chapter 2) is one that abstracts from monetaryfrictions, in order to focus attention on more essential aspects of the mon-etary transmission mechanism, such as the way that spending decisions de-pend on expected future interest rates as well as current ones or the way inwhich fluctuations in nominal expenditure affect real activity. I then pauseat various points to consider the modifications of the analysis that are re-quired in order to take account of the monetary frictions that evidentlyexist, given the observation that non-interest-earning currency continuesto be held. It is shown that, as a quantitative matter, these modifications areof relatively minor importance.In the discussion of interest-rate determination under a present-day

channel system, I have supposed that there is a demand for at least a smallquantity of central-bank balances for clearing purposes, and these are helddespite the existence of a small opportunity cost (25 basis points on aver-age). But once the idea has been accepted that the central bank can varythe overnight interest rate without ever having to vary the size of this returnspread, the functioning of the system no longer depends on the existenceof a clearing demand. Consider instead the supposition that balances heldwith the central bank cease to be any more useful to commercial banks thanany other equally riskless overnight investment. In this case, the demand forcentral-bank balances is zero for all interest rates higher than the depositrate idt . But banks should still be willing to hold arbitrary balances at thecentral bank as long as the market overnight rate is no higher than therate paid by the central bank. In this case, it would no longer be possibleto induce the overnight cash market to clear at a target rate higher thanthe rate paid on overnight balances at the central bank; for equation (3.1)reduces to it = idt in the case of any positive supply of central-bank balances.


But the central bank could still control the equilibrium overnight rate, byusing the deposit rate as its policy instrument.20 Such a system would differfrom current channel systems in that an overnight lending facility wouldno longer be necessary, so that there would no longer be a “channel.”21

Furthermore, the rate paid on central-bank balances would no longer beset at a fixed spread δ below the target overnight rate, but rather at exactlythe target rate.Perfect control of overnight rates should still be possible through adjust-

ments of the rate paid on overnight central-bank balances, and changes inthe target overnight rate would not have to involve any change in the tar-get supply of central-bank balances, just as is true under current channelsystems. Indeed, in this extreme case, any variations that did occur in thesupply of central-bank balances would cease to have any effect at all uponthe equilibrium overnight rate.But how can interest-rate variation be achieved without any adjustment at

all of the supply of central-bank balances? Informal discussions often treatinterest-rate control by the central bank like a species of price control. Cer-tainly, if a government decides to peg the price of some commodity, it maybe able to do so, but only by holding stocks of the commodity that are suffi-ciently large relative to its world market, and by standing ready to vary thoseholdings by large amounts as necessary. If the market in question is a largeone (more to the point, if either supply or demand in themarket is relativelyprice elastic) relative to the size of the balance sheet of the government en-tity seeking to control the price, one doubts that such efforts will be effec-tive. What is different about controlling short-term nominal interest rates?The difference is that there is no inherent “equilibrium” level of in-

terest rates to which the market would tend in the absence of central-bank intervention and against which the central bank must therefore exerta significant countervailing force in order to achieve a given operating

20. Grimes (1992)makes a related point, showing that variation of the interest rate paid oncentral-bank balances would be effective in an environment in which central-bank reserves areno more useful for carrying out transactions than other liquid government securities, so thatopen-market purchases or sales of such securities are completely ineffective. Hall (1983, 2002)has also proposed this as a method of price-level control in the complete absence of monetaryfrictions. Hall speaks of control of the interest yield on a government “security,” without anyneed for a central bank at all. But because of the special features that this instrument wouldneed to possess, which are not possessed by privately issued securities—it is a claim only tofuture delivery of more units of the same instrument, and society’s unit of account is definedin terms of this instrument—it seems best to think of it as still taking the same institutionalform that it does today, namely, balances in an account with the central bank.21. This presumes a world in which no payments are cleared using central-bank balances.

Of course, there would be no harm in continuing to offer such a facility as long as the central-bank clearing system were still used for at least some payments.


target.22 This is because there is no inherent value (in terms of real goodsand services) for a fiat unit of account such as the “dollar,” except insofar asa particular exchange value results from the monetary policy commitmentsof the central bank. The basic point was clear to Wicksell (1898, pp. 100–101), who compares relative prices to a pendulum that always returns to thesame equilibriumposition when perturbed, while themoney prices of goodsin general are compared to a cylinder resting on a horizontal plane, whichcan remain equally well in any location on the plane to which it may happento be moved.23 Alternative price-level paths are thus equally consistent withmarket equilibrium in the absence of any intervention that would vary thesupply of any real goods or services to the private sector; and associated withthese alternative paths for the general level of prices are alternative pathsfor short-term nominal interest rates.Of course, this analysis might suggest that while central banks can bring

about an arbitrary level of nominal interest rates (by creating expectationsof the appropriate rate of inflation), they should not be able to significantlyaffect real interest rates, except through trades that are large relative to theeconomy that they seek to affect. It may also suggest that they should beable tomove nominal rates only by altering inflation expectations; yet banksgenerally do not feel that they can easily alter expectations of inflation overthe near term, so that one might doubt that they should be able to affectshort-term nominal rates through such a mechanism.However, once one recognizes that many prices (and wages) are fairly

sticky over short time intervals, the arbitrariness of the path of nominalprices (in the sense of their underdetermination by real factors alone)implies that the path of real activity and the associated path of equilibriumreal interest rates are equally arbitrary. It is equally possible, from a logicalstandpoint, to imagine allowing the central bank to determine, by arbitraryfiat, the path of aggregate real activity, or the path of real interest rates, orthe path of nominal interest rates as it is to imagine allowing it to determinethe path of nominal interest rates.24 In practice, it is easiest for central

22. This does not mean that Wicksell’s notion of a natural rate of interest determined byreal factors is of no relevance to the consideration of the policy options facing a central bank. Itis indeed, as argued in Chapter 4. But the natural rate of interest is the rate of interest requiredfor an equilibrium with stable prices; the central bank nonetheless can arbitrarily choose the levelof interest rates (within limits), because it can choose the degree to which prices will increaseor decrease.23. This is the grounds for his argument—in the quotation from the introduction to

his book that begins this chapter—that control of the general level of prices involves nointerference with the market mechanism of the kind that is required if some relative priceis to be controlled.24. This does not mean, of course, that absolutely any paths for these variables can be

achieved throughmonetary policy; the chosen pathsmust be consistent with certain constraints


banks to exert relatively direct control over overnight nominal interest rates,and so they generally formulate their short-run objectives (their operatingtarget) in terms of the effect that they seek to bring about in this variablerather than in one of the others.Even recognizing the existence of a very large set of rational-expectations

equilibria—equally consistent with optimizing private-sector behavior andwith market clearing, in the absence of any specification of monetary policy—one might nonetheless suppose, as Fischer Black (1970) once did, thatin a fully deregulated system the central bank should have no way of us-ing monetary policy to select among these alternative equilibria. The pathof money prices (and similarly nominal interest rates, nominal exchangerates, and so on) would then be determined solely by the self-fulfilling ex-pectations of market participants. Why should the central bank play anyspecial role in determining which of these outcomes should actually occurif it does not possess any monopoly power as the unique supplier of somecrucial service?The answer is that the unit of account in a purely fiat system is defined

in terms of the liabilities of the central bank.25 A financial contract thatpromises to deliver a certain number of U.S. dollars at a specified futuredate is promising payment in terms of Federal Reserve notes or clearingbalances at the Fed (which are treated as freely convertible into one anotherby the Fed). Even in the technological utopia imagined by the enthusiasts ofelectronicmoney—where financial-market participants are willing to acceptas final settlement transfers made over electronic networks in which thecentral bank is not involved—if debts are contracted in units of a nationalcurrency, then clearing balances at the central bank still define the thing towhich these other claims are accepted as equivalent.This explains why the nominal interest yield on clearing balances at the

central bank can determine overnight rates in the market as a whole. Thecentral bank can obviously define the nominal yield on overnight depositsin its clearing accounts as it chooses; it is simply promising to increase thenominal amount credited to a given account, after all. It can also determine

implied by the conditions for a rational-expectations equilibrium, e.g., those presented inChapter 4. But this is true even in the case of the central bank’s choice of a path for the pricelevel. Even in a world with fully flexible wages and prices, for instance, it would not be possibleto bring about a rate of deflation so fast as to imply a negative nominal interest rate.25. See Hall (2002) and White (2001) for expressions of similar views. White emphasizes

the role of legal-tender statutes in defining the meaning of a national currency unit. But suchstatutes do not represent a restriction upon the means of payment that can be used withina given geographical region—or at any rate, there need be no such restrictions upon privateagreements for the point to be valid. What matters is simply what contracts written in terms ofa particular unit of account are taken to mean, and the role of law in stabilizing such meaningsis essentially no different than, say, in the case of trademarks.


this independently of its determination of the quantity of such balances thatit supplies. Commercial banks may exchange claims to such deposits amongthemselves on whatever terms they like. But the market value of a dollardeposit in such an account cannot be anything other than a dollar—becausethis defines the meaning of a “dollar”!This places the Fed in a different situation than any other issuer of dollar-

denominated liabilities.26 Citibank can determine the number of dollarsthat one of its jumbo CDs will be worth at maturity, but must then allowthe market to determine the current dollar value of such a claim; it cannotdetermine both the quantity that it wishes to issue of such claims and the in-terest yield on them. Yet the Fed can, and does so daily—though at present itchooses to fix the interest yield on Fed balances at zero and only to vary thesupply. The Fed’s current position as monopoly supplier of an instrumentthat serves a special function is necessary in order for variations in the quan-tity supplied to affect the equilibrium spread between this interest rate andother market rates, but not in order to allow separate determination of theinterest rate on central-bank balances and the quantity of them in existence.Yes, some may respond, a central bank would still be able to determine

the interest rate on overnight deposits at the central bank, and thus theinterest rate in the interbankmarket for such claims, even in a world of com-pletely frictionless financial markets. But would control of this interest ratenecessarily have consequences for other market rates, the ones that matterfor critical intertemporal decisions such as investment spending? The an-swer is that it must—and all the more so in a world in which financial mar-kets have become highly efficient, so that arbitrage opportunities created bydiscrepancies among the yields on different market instruments are imme-diately eliminated. Equally riskless short-term claims issued by the privatesector (say, shares in a money-market mutual fund holding very short-termTreasury bills) would not be able to promise a different interest rate thanthe one available on deposits at the central bank; otherwise, there would

26. Costa and De Grauwe (2001) instead argue that “in a cashless society . . . the centralbank cannot ‘force the banks to swallow’ the reserves it creates” (p. 11), and speak of the centralbank being forced to “liquidate . . . assets” in order the redeem the central-bank liabilities thatcommercial banks are “unwilling to hold” in their portfolios. This neglects the fact that thedefinition of the U.S. dollar allows the Fed to honor a commitment to pay a certain numberof dollars to account holders the next day by simply crediting them with an account of thatsize at the Fed—there is no possibility of demanding payment in terms of some other assetvalued more highly by the market. Similarly, Costa and De Grauwe argue that “the problem ofthe central bank in a cashless society is comparable to [that of a] central bank pegging a fixedexchange rate” (footnote 15). But the problem of a bank seeking tomaintain an exchange-ratepeg is that it promises to deliver a foreign currency in exchange for its liabilities, not liabilitiesof its own that it freely creates. Costa and De Grauwe say that they imagine a world in which“the unit of account remains a national affair . . . and is provided by the state” (p. 1), but seemnot to realize that this means defining that unit of account in terms of central-bank liabilities.

4. Interest-Rate Rules 37

be an excess supply or demand for the private-sector instruments. More-over, determination of the overnight interest rate would also have to implydetermination of the equilibrium overnight holding return on longer-livedsecurities, up to a correction for risk; and so determination of the expectedfuture path of overnight interest rates would essentially determine longer-term interest rates.The special feature of central banks, then, is simply that they are entities

whose liabilities happen to be used to define the unit of account in a widerange of contracts that other people exchange with one another. There isperhaps no deep, universal reason why this need be so; it is certainly not es-sential that there be one such entity per national political unit. Nonetheless,the provision of a well-managed unit of account—one in terms of which theequilibrium prices of many goods and services are relatively stable—clearlyfacilitates economic life. Furthermore, given the evident convenience ofhaving a single unit of account used by most of the parties with whom onewishes to trade, one may well suppose that this function should properlycontinue to be taken on by the government, even in a world of highly effi-cient information processing. I assume here a world in which central banks(whether national or supranational, as in the case of the ECB) continue tofulfill this function, and in which they are interested in managing their fiatcurrency in the public interest. The present study aims to supply a theorythat can help them to do so.

4 Interest-Rate Rules

I have argued that the central problem of the theory of monetary policy is toprovide principles that can be used in selecting a desirable rule for settinga central bank’s interest-rate operating target. It is perhaps worth saying abit more at this point about exactly what form of rules I have in mind andwhat sort of questions I would like to answer about them. This will provide amore concrete background for the analysis to be developed in the chaptersto come.Probably the earliest example of a prescription for monetary policy in

terms of an interest-rate rule is due to Wicksell (1898, 1907). Although writ-ing at a time when the leading industrial nations remained committed to thegold standard, with evenmost scholars assuming the necessity of a commod-ity standard of one sort or another, Wicksell foresaw the possibility of a purefiat standard and indeed argued that it was essential for the developmentof “a rational monetary system.” The soundness of his advocacy of price-level targeting in the context of a pure fiat monetary standard was shownduring the 1930s, when Sweden abandoned the gold standard that had be-come an engine of worldwide deflation. The Swedish Riksbank adopted aprice-level target as a substitute and used its interest-rate policy to achieve


this target as recommended by Wicksell. The policy was quite successful,especially in comparison with the price-level fluctuations suffered by manyother countries during this period ( Jonung, 1979). Nonetheless, the exper-iment was radical for its time and was not to be repeated for another 50years.27

Wicksell advocated not only price-level targeting, but a specific form ofinterest-rate rule for the management of such a system. His original (1898)statement of the proposed rule was as follows:

So long as prices remain unaltered the [central] banks’ rate of interest28 isto remain unaltered. If prices rise, the rate of interest is to be raised; andif prices fall, the rate of interest is to be lowered; and the rate of interestis henceforth to be maintained at its new level until a further movementof prices calls for a further change in one direction or the other (p. 189,italicized in original).

Wicksell’s proposal can be represented mathematically as a commitmentto set the central bank’s interest-rate operating target it according to arelation of the form29

it = ı̄ + φpt , (4.1)

where pt is the log of some general price index (the one that the policy aimsto stabilize) and φ is a positive response coefficient, or alternatively by a ruleof the form

it = φπt (4.2)

where πt ≡ pt is the inflation rate.30 I discuss price-level determinationunder policy rules of this kind in Chapter 2 and argue that such a rule

27. For an example of favorable academic comment on the Swedish experiment at thetime, see Fisher (1934, pp. 399–410).28. In the passage quoted here, Wicksell proposes a coordinated policy by the world’s

central banks in order to establish a stable world unit of account. Elsewhere he offers similaradvice for the stabilization of the value of a single national unit of account.29. Wicksell proposes nothing so specific as a log-linear relation of this kind, of course; he

only describes a monotonic relationship. The log-linear specification is useful for the simplecalculations of the next section. In Chapter 2, I discuss the usefulness of this sort of log-linearapproximation of what is necessarily not a globally log-linear rule. The specification (4.1)cannot be maintained for all possible price levels, owing to the requirement that the nominalinterest rate be nonnegative.30. Note that a commitment to set the interest rate according to (4.2) from some date t 0

forward is equivalent to a commitment to set it according to a rule of the form (4.1), wherethe intercept ı̄ corresponds to it 0−1 − φpt 0−1. Fuhrer and Moore (1995c) propose a morecomplicated interpretation of Wicksell’s proposal, in which the interest change is instead a


should indeed succeed in stabilizing the price index around a constantlevel. The principles that determine the equilibrium price level under sucha regime are briefly sketched in Section 4.3 of this introduction.A simple Wicksellian rule such as this has certain advantages as well, at

least in comparison to other equally simple rules, as discussed by Giannoni(2000). Nonetheless, I do not confine my attention to rules of this kind. Myprimary interest in this study is in the analysis of proposals that are closer inform to the policies currently followed by many central banks. These rulesinvolve an (explicit or implicit) target for the inflation rate, rather than forthe price level; nor are they expressible solely in terms of interest-rate changes,so that they are equivalent to a rule that responds to the price level, as inthe case of (4.2). The rules typically allow for “base drift” in the price levelas a result—even if the inflation rate is kept within a narrow interval at alltimes, there is no long-run mean reversion in the price level, or even inthe price level deflated by some deterministic target path. Moreover, as Ieventually conclude in Chapter 8, optimal interest-rate rules are likely tohave this property.

4.1 Contemporary Proposals

The best-known example of a proposed rule for setting interest rates is prob-ably the one proposed by John Taylor (1993), both as a rough descriptionof the way that policy had actually been made by the U.S. Federal Reserveunder Alan Greenspan’s chairmanship and as a normative prescription (onthe basis of stochastic simulations using a number of econometric models).According to the Taylor rule, as it has come to be known, the Fed’s funds-rate operating target it is set as a linear function of measures of the currentinflation rate and the current gap between real output and potential:

it = 0.04 + 1.5(π̄t − 0.02)+ 0.5(yt − ypt

), (4.3)

where π̄t is the rate of inflation (the change in the log GDP deflator overthe previous four quarters in Taylor’s illustration of the rule’s empirical fit),yt is log output (log real GDP in Taylor’s plot), and y

pt is log “potential”

output (log real GDP minus a linear trend in Taylor’s plot). The constantsin Taylor’s numerical specification indicate an implicit inflation target of 2percent per annum, and an estimate of the long-run real federal funds rateof 2 percent per annum as well, so that a long-run average inflation rateat the target requires a long-run average funds rate of 4 percent. A slightly

function of the price level.While their rule is slightly more difficult to analyze, it does not leadto substantially different conclusions about the consequences of commitment to a Wicksellianrule.


simpler rule in the same vein was proposed for the United Kingdom byCharles Goodhart (1992), according to which “there should be a presump-tion” that the nominal interest rate would satisfy an equation of the form

it = 0.03+ 1.5 π̄t ,and “the Governor should be asked, say twice a year, to account for anydivergence from that ‘rule’ ” (p. 324).The coefficients 1.5 and 0.5 in the Taylor rule are round figures argued

to approximately characterize U.S. policy between 1987 and 1992 and thatwere found to result in desirable outcomes (in terms of inflation and outputstability) in simulations.31 In Taylor’s discussions of the rule, he places partic-ular stress upon the importance of responding to inflation above the targetrate by raising the nominal interest-rate operating target by more than theamount by which inflation exceeds the target; the importance of this “Tay-lor principle” is considered in detail in Chapters 2 and 4. Taylor (1999c)argues that the Fed did not adhere to this principle before 1979 (at whichtime Fed chairman Paul Volcker instituted a radical shift in policy), and thisfailure may well have been responsible for the greater U.S. macroeconomicinstability during the 1960s and 1970s. Taylor illustrates the change in policyby estimating simple Fed reaction functions of the form

it = ı̄ + φπ(π̄t − π̄)+ φxxt (4.4)

for two different sample periods, using ordinary least squares; his coefficientestimates are shown in Table 1.1. (Here I introduce the notation xt for theoutput gap, again equated with deviations of log real GDP from trend inTaylor’s empirical work.) Nelson (2001) finds that estimates of Taylor-typerules for the United Kingdom tell a similar story. Prior to the adoption ofinflation targeting in 1992, U.K. interest rates rose less than one-for-one withincreases in inflation (and in the mid-1970s responded little or not at all),but since 1992, the long-run inflation response coefficient is estimated tohave been nearly 1.3.Estimates of empirical central-bank reaction functions typically find that

a dynamic specification fits the data better, whatever the validity may be ofTaylor’s (1999b) preference for a purely contemporaneous specification onnormative grounds.32 For example, Judd and Rudebusch (1998) estimate

31. A similar form of policy rule was advocated, also on the basis of simulation studies, ataround the same time by Henderson and McKibbin (1993).32. This is also true of the estimates for the United Kingdom reported in Nelson (2001).

This is why I refer to Nelson’s “long-run inflation response coefficient” in the previous para-graph, rather than to a contemporaneous response coefficient of the kind estimated by Taylor(1999c).


TABLE 1.1 Alternative estimates of Fed reaction functionsa

φπ (s.e.) φx (s.e.) γ ρ1 (s.e.) ρ2 (s.e.)

Taylor (1999c)1960–1979 0.81 (.06) 0.25 (.05)1987–1997 1.53 (.16) 0.77 (.09)

Judd-Rudebusch (1998)1979–1987 1.46 (.26) 1.53 (.80) 1 0.56 (.12)1987–1997 1.54 (.18) 0.99 (.13) 0 0.72 (.05) 0.43 (.10)

Clarida et al. (2000)1960–1979 0.83 (.07) 0.27 (.08) 0.68 (.05) *1979–1996 2.15 (.40) 0.93 (.42) 0.79 (.04) *

Orphanides (2003)1966–1979 1.49 (.38) 0.46 (.13) 0.68 (.07) 0.26 (.14)1979–1995 1.89 (.64) 0.18 (.20) 0.77 (.10) 0.08 (.19)

a Asterisks indicate values not constrained to be zero in the estimation, but not reported in thepublished account of regression results.

Fed reaction functions according to which the funds-rate operating targetadjusts in response to changes in an implicit desired level of the funds rateı̄ t according to partial-adjustment dynamics of the form33

it = (1− ρ1)̄ıt + ρ1it−1 + ρ2(it−1 − it−2). (4.5)

The desired level of the funds rate in turn depends upon inflation and theoutput gap in a manner similar to that postulated by Taylor,

ı̄ t = ı̄ + φπ(π̄t − π̄)+ φx(xt − γ xt−1), (4.6)

except that the allowance for nonzero γ means that the desired funds ratemay respond to the rate of change of the output gap as well as (or insteadof) its level. The Judd-Rudebusch estimated coefficients for two differentsample periods, corresponding to the Fed chairmanships of Paul Volckerand Alan Greenspan, respectively, are also reported in Table 1.1.34 Taylor’sview of the nature of policy in the Greenspan period is largely confirmed,with the exception that Judd and Rudebusch estimate partial-adjustment

33. Here as in all other regressions reported in this section, periods are assumed to bequarters, and quarterly data are used in the estimation.34. In their preferred estimates, the value of γ is imposed rather than estimated. The ex-

treme values assumed for the separate periods, however, are suggested by preliminary regres-sions in which the value of γ is unconstrained.


dynamics implying substantial persistence. They give a similar characteriza-tion of policy in the Volcker period, except that the desired funds rate isfound to depend on the rate of change of the output gap, rather than itslevel.35

Many recent discussions of central-bank behavior, both positive and nor-mative, argue instead for specifications in which a bank’s operating targetdepends on forecasts. For example, Clarida et al. (2000) estimate Fed reac-tion functions of the form36

ı̄ t = ı̄ + φπE[πt+1 − π̄ |�t]+ φxE[xt |�t], (4.7)

where�t is the information set assumed to be available to the Fed when set-ting it , and the actual operating target is again related to the desired fundsrate ı̄ t through partial-adjustment dynamics. Like Taylor, these authors findan important increase in the degree to which the Fed’s desired level forthe funds rate responds to inflation variations since 1979, though in theirspecification the Fed responds to an inflation forecast rather than inflationthat has already occurred.37

Finally, it should be noted that the view that the Fed has responded morevigorously to inflation variations since 1979 has not gone unchallenged. Or-phanides (2003) argues that the findings of Taylor and the other authorsjust cited are distorted by the use of inflation and output-gap data (especiallythe output-gap estimates), which were not available to the Fed at the timethat its interest-rate decisions were made. When he estimates Fed reactionfunctions of the kind assumed by Clarida et al. using the forecasts actuallyproduced by Fed staff at the time rather than econometric projections us-ing the data available now, he obtains much more similar estimates for thepre-Volcker and post-Volcker periods, as shown in Table 1.1. The inflation-response coefficient φπ is well above one in both periods, according to Or-phanides’s estimates; he instead emphasizes the reduction in the size of φxas the crucial policy change after 1979, and the key to U.S. macroeconomic

35. Judd and Rudebusch also estimate a reaction function for the period (1970–1978)corresponding to the chairmanship of Arthur Burns. Like Taylor, in this period they estimatean inflation-response coefficient φπ less than one, though not significantly so in their case.36. Clarida et al. also estimate variants of the rule in which the forecast horizon is assumed

to be more than one quarter in the future. The policies of inflation-targeting central bankshave often been represented by rules in which the interest-rate operating target responds to aforecast of inflation as many as 8 quarters in the future. See, e.g., Black et al. (1997b), Batiniand Haldane (1999).37. Like Taylor, they also suggest that this change has led to greater macroeconomic sta-

bility in the later period. They provide a theoretical analysis of why this could have been so,in terms of the vulnerability of an economy to instability due to self-fulfilling expectations inthe case of a policy rule of the kind that they estimate for the period 1960–1979. Reasons forthis are discussed in Chapter 4.


stability since the mid-1980s. I do not seek to resolve this debate about his-torical Fed policy here, but simply note that much current debate aboutboth the explanation of recent U.S. policy successes and the reason for pastpolicy failures turns upon claims concerning the desirability of particularcoefficients in Taylor-type rules.These alternative characterizations suggest a number of questions about

the form of a desirable interest-rate rule. One obvious question is whetherthe variables to which the Fed is described as responding in the Taylorrule and the estimated reaction functions just discussed—some measuresof inflation and the output gap—are ones that make sense. Is it desirablefor interest rates to be adjusted in response to variations in these variables,and with the signs proposed by Taylor? Are there any grounds for thinkingit more important to respond to variations in these variables than in others?Is responding to variations in these variables an adequate substitute forattempting to respond to the underlying disturbances that are perceivedto be currently affecting the economy?If it does make sense to respond to these variables, how exactly should

they be defined? Which sort of price index is most appropriately used in theinflation measure? Relative to what concept of potential output should theoutput gap measure be defined? And how strongly is it desirable to respondto variations in these variables? Is a value of φπ greater than one essential, asargued by Taylor? Is a large value of φx dangerous, as argued byOrphanides?I am also interested in the most desirable dynamic specification of such

an interest-rate rule. Are purely contemporaneous responses, as prescribedby Taylor, preferable? Is there any justification for the more inertial interest-rate dynamics indicated by the estimated reaction functions? If so, howinertial is it desirable for interest-rate policy to be? Is it preferable to respondto forecasts rather than to current or past values of inflation and the outputgap? If so, how far in the future should the forecasts look?Another type of policy rule that has figured prominently both in recent

descriptions of actual central-bank behavior and in normative prescriptionsis an inflation-forecast targeting rule. A classic example is the sort of rule thatis often used to explain the current procedures of the Bank of England(e.g., Vickers, 1998). According to the formula, the Bank should be willingto adopt a given operating target it for the overnight interest rate at date tif and only if the Bank’s forecast of the evolution of inflation over the next2 years, conditional upon the interest rate remaining at the level it , impliesan inflation rate of 2.5 percent per annum (the Bank’s current inflationtarget) 2 years after date t . This is an example of what Svensson (1999,2003b) calls a “targeting rule” as opposed to an instrument rule. No formulais specified for the central bank’s interest-rate operating target. Rather, it isto be set at whatever level may turn out to be required in order for thebank’s projections to satisfy a certain target criterion. That criterion need


not involve only future inflation; for example, Svensson (1999) advocates aflexible inflation-targeting rule in which the interest rate is adjusted at datet so as to ensure that

Etπt+j + λEtxt+k = π̄, (4.8)

where π̄ is the average inflation target, the coefficient λ > 0 depends onthe relative importance of output-gap stabilization, and the horizons j andk are not necessarily the same distance in the future.I also wish to consider the desirable specification of a target criterion in

the case of a policy rule of this sort. Again, a basic question is whether itmakes sense to define the target criterion in terms of projections for theseparticular variables, inflation and the output gap, rather than others, suchas monetary aggregates. If so, what should determine the relative weight,if any, to be placed on the output-gap forecast? How far into the futureshould the forecasts in the target criterion look? And is a desirable criterionpurely forward looking, as in the case of the two examples just mentioned, orshould the inflation target be history dependent, in addition to (possibly)depending on projected future output gaps?This study will seek to elaborate a methodology that can be used to give

quantitative answers to questions of this sort about optimal policy rules. Ofcourse, the answers obtained depend on the details of what one assumesabout the nature of the monetary transmission mechanism, and I do notpropose to argue for a specific quantitative rule. The aim of the presentstudy ismore to suggest a way of approaching the problem than to announcethe details of its solution. However, certainmodel elements recur inmany ofthe models currently used in studies of the effects of monetary policy, bothin the academic literature and in central banks; and given the likelihoodthat a reasonable model is judged to include these features, I may obtainsome tentative conclusions as to the likely form of reasonable policy rules.

4.2 General Criticisms of Interest-Rate Rules

Before taking up specific questions of these kinds about the form of de-sirable interest-rate rules, it is first necessary to address some more basicissues. Would any form of interest-rate rule represent a sensible approachto monetary policy? Proponents of monetary targeting have often arguedagainst interest-rate control as such—asserting not that skill is required inthe choice of an interest-rate operating target, but that it is a serious mistaketo have one at all.One famous argument, mentioned previously, is that of Sargent andWal-

lace (1975). These authors consider a general class of money-supply ruleson the one hand, and a general class of interest-rate rules on the other,


and argue that while any of the money-supply rules leads to a determinaterational-expectations equilibrium (in the context of a particular rational-expectations IS-LM model), none of the interest-rate rules do. By determi-nacy of the equilibrium I mean that there is a unique equilibrium satisfy-ing certain bounds, made precise in Chapter 2. Sargent and Wallace arguethat interest-rate rules lead to indeterminacy, meaning that even if one re-stricts one’s attention to bounded solutions to the equilibrium relations (asI largely do in this study), there is an extremely large set of equally possibleequilibria. These include equilibria in which endogenous variables such asinflation and output respond to random events that are completely unre-lated to economic “fundamentals” (i.e., to the exogenous disturbances thataffect the structural relations that determine inflation and output) and alsoequilibria in which “fundamental” disturbances cause fluctuations in equi-librium inflation and output that are arbitrarily large relative to the degreeto which the structural relations are perturbed. Thus in such a case, macro-economic instability can occur owing purely to self-fulfilling expectations.This is plainly undesirable, if one’s objective is to stabilize inflation and/oroutput.38 Hence Sargent and Wallace argue that interest-rate rules can beexcluded from consideration as a class; the problem of optimal monetarypolicy is then properly framed as a question of what the best money-supplyrule would be.However, as McCallum (1981) notes, the Sargent-Wallace indeterminacy

result applies, even in the context of their own model, only in the case ofinterest-rate rules that specify an exogenous evolution for the nominal in-terest rate. This includes the possibility of rules that specify the nominalinterest rate as a function of the history of exogenous disturbances, but notrules that make the nominal interest rate a function of endogenous variables,such as inflation or output. Yet the Taylor rule, and the other interest-raterules discussed previously, are all rules of the latter sort, so that the Sargent-Wallace result need not apply. The same is shown to be true, in Chapters 2and 4, in the case of the optimizing models of inflation and output determi-nation considered here. Indeed, I find that, at least in the case of the simplemodel of the monetary transmission mechanism that is most extensively an-alyzed here, either the type of feedback from the general price level to theinterest rate (or from changes in the price level to changes in the interestrate) advocated by Wicksell or the type of feedback from inflation and out-put to the central bank’s interest-rate operating target prescribed by Taylorwould suffice to imply a determinate rational-expectations equilibrium. In

38. The point remains valid if one’s objective is, as I argue that it should be, to stabilizeoutput relative to its natural rate, rather than output stabilization as such. For the fluctuationsin output owing purely to self-fulfilling expectations will imply fluctuations in the output gapas well.


the case of a level-to-level (or change-to-change) Wicksellian specification,it is only necessary that the sign of the response be the one advocated byWicksell. In the case of a change-to-level specification such as that proposedby Taylor, the Taylor principle mentioned earlier—the requirement that asustained increase in inflation eventually result in an increase in nominalinterest rates that is even larger in percentage points—turns out to be thecritical condition that determines whether equilibrium should be determi-nate or not.39

A related criticism of interest-rate targeting alsomaintains that such a pol-icy is dangerous because it allows instability to be generated by self-fulfillingexpectations, but is not based on the possibility of multiple rational-expec-tations equilibria. Friedman (1968) argues that attempting to control nomi-nal interest rates is dangerous on the basis ofWicksell’s (1898, 1907) famousanalysis of the “cumulative process.” With a nominal interest rate that isfixed at a level below the natural rate, inflation is generated that increasesinflation expectations, which then stimulates demand even further owingto the reduction in the real rate, generating even faster inflation, furtherincreasing inflation expectations, and so on without bound.40 The same pro-cess should occur with the opposite sign if the interest rate happens to beset above the natural rate; thus any attempt to fix the nominal interest ratewould seem almost inevitably to generate severe instability of the inflationrate. (In Friedman’s analysis, there is no indeterminacy of the path of in-flation, as inflation expectations are assumed to be a specific function ofpreviously observed inflation.)As is discussed in Chapter 4, this analysis can be formalized in the context

of an optimizing model in which inflation and income forecasts are basedon extrapolation from past data (e.g., using empirical time-series models).But once again, the classic analysis applies only in the case of a policy thatexogenously specifies the path of nominal interest rates. If instead a surgein inflation and output leads to increases in nominal interest rates largeenough to raise real rates, then demand should be damped, tending tolower inflation as well—so that there should be no explosive instability of ei-ther inflation or output dynamics under adaptive learning. Indeed, the anal-yses of Bullard and Mitra (2002) and Preston (2002a) find that conformity

39. Clarida et al. (2000) argue on this basis that the macroeconomic instability of the 1970sin the United States may have been increased by self-fulfilling expectations, given that theirestimates (see Table 1.1) imply that the Taylor principle has been satisfied by post-1979 policybut not by previous policy.40. This summarizes Friedman’s account, rather than Wicksell’s original discussion. Wick-

sell does not discuss endogenous inflation expectations and so concludes that the price levelrather than the inflation rate should rise without bound. Lindahl (1939) was the first to intro-duce endogenous inflation expectations into the analysis and so to conclude that the inflationrate could rise without bound.


to the Taylor principle is both a necessary and sufficient condition (at leastwithin certain simple classes of policy rules) for adaptive learning dynam-ics to converge to a stationary rational-expectations equilibrium, in whichinflation and output fluctuate only in response to “fundamentals.”Thus it is important to realize that these well-known criticisms of interest-

rate targeting assume that under such a policy the interest-rate target wouldremain fixed, regardless of the path of inflation. The analyses are quiteinapplicable in the case of policy rules such as Wicksell’s rule, the Taylorrule, or typical inflation-forecast targeting rules, which require that interestrates be raised sharply if inflation is either observed or forecasted to exceedthe target rate consistently for a substantial period of time. In fact, in theseconventional arguments for monetary targeting, the reason for control ofmoney growth is precisely that this is a policy commitment that ensures thatan excessive rate of inflation will lead to interest-rate increases sufficient tocurb the growth of nominal expenditure. A fixed target path for the moneysupply (or more generally, a path that is contingent only upon exogenousstate variables, not upon the path of the price level) implies that if the pricelevel grows more rapidly, the private sector will be forced to operate with alower level of real money balances. This will require interest-rate increasesand/or a reduction in real activity sufficient to reduce desired real moneybalances to the level of the real money supply.But the same kind of automatic increase in interest rates, curbing expen-

diture, can be arranged through a simple commitment of the central bankto raise interest rates in response to deviations of the general level of pricesfrom its desired path, as first proposed by Wicksell. Moreover, once one rec-ognizes that quantity control is not necessary for such a system to work, it ishard to see why one should wish to be encumbered by it. Over the courseof the twentieth century, it came to be accepted that no convertibility ofnational currencies into a real commodity such as gold was necessary inorder for central banks to act in a way that controlled the value of their cur-rencies. Moreover, once this was accepted, it quickly became evident thatnations were better off not relying upon such a crude mechanism as a goldstandard, which left the value of the national unit of account vulnerable tofluctuations in the market for gold. Similarly, once one accepts that the ad-justment of interest rates to head off undesired price-level variation can bemanaged by central banks without any need for so mechanical a disciplineas is provided by a money-growth target, it should be clear that a properlychosen interest-rate rule can be more efficient than monetary targeting,which has the unwanted side effect of making interest rates (and hencethe pace of aggregate expenditure) vulnerable to variations in the relationbetween desired money balances and the volume of transactions.A more subtle criticism of interest-rate rules as an approach to systematic

monetary policy would argue that even if such rules lead to well-defined,


well-behaved equilibria, the description of policy in this way may still not beuseful to a central bank that wishes to understand, and thus to accuratelycalibrate, the consequences of its actions. It is often supposed that the keyto understanding the effects of monetary policy on inflation must alwaysbe the quantity theory of money, according to which the price level is de-termined by the relation between the nominal money supply, on the onehand, and the demand for real money balances, on the other. It may thenbe concluded that what matters about any monetary policy is the impliedpath of the money supply, whether this is determined through straightfor-ward monetary targeting or in some more indirect manner.41 From such aperspective, it might seem that a clearer understanding of the consequencesof a central bank’s actions would be facilitated by an explicit focus on whatevolution of the money supply the bank intends to bring about—that is,by monetary targeting—rather than by talk about interest-rate policy that,even if it does imply a specific path for the money supply, does not makethe intended path entirely transparent.The present study aims to show that the basic premise of such a criticism

is incorrect. One of the primary goals of Part I of this book is the develop-ment of a theoretical framework in which the consequences of alternativeinterest-rate rules can be analyzed, which does not require that they firstbe translated into equivalent rules for the evolution of the money supply.Indeed, much of the time I analyze the consequences of interest-rate ruleswithout having to solve for the implied path of the money supply, or evenhaving to specify the coefficients of a “money-demand” relation. In the caseof an economy without monetary frictions—a case that I argue is an ana-lytically convenient approximation for many purposes, and that may wellrepresent the future, as discussed earlier—there will not even be any mean-ingful money supply or demand to be defined. If instead one takes accountof the sort of frictions that evidently still exist in an economy like that of theUnited States at present, then the models imply an equilibrium path for themoney supply along with other endogenous variables. But the factors deter-mining the equilibrium paths of both inflation and output continue to benearly the same as in the frictionless economy, so that it does not seem at allnatural or useful to try to explain the predicted paths of inflation and outputas consequences of the implied path of the money supply. Instead, it provesto be possible to discuss the determinants of inflation and output in a fairlystraightforward way in terms of the coefficients of an interest-rate rule. Thusthe characterizations of central-bank policy offered previously are found tobe quite convenient for analysis of the consequences of one quantitativespecification or another. I further show, in Chapter 8, that optimal policy

41. This is, e.g., the perspective taken in the Monetary History of Friedman and Schwartz(1963).


can be conveniently represented in terms of specifications of exactly thissort, leading to answers to the very specific questions about interest-ratepolicy posed in the previous section.

4.3 Neo-Wicksellian Monetary Theory

The non-quantity-theoretic analytical framework developed here developsseveral important themes from the monetary writings of Knut Wicksell(1898, 1906, 1907, 1915). Wicksell argued that even the variations in theprice level observed in his own time, under the international gold stan-dard, were not primarily due to variations in the world gold supply, butrather to two other factors—the policies followed by central banks, adjust-ing the “bank rate” at which they were willing to discount short-term bills,on the one hand, and real disturbances, affecting the natural rate of inter-est, on the other. In Wicksell’s view, price stability depended on keepingthe interest rate controlled by the central bank in line with the natural ratedetermined by real factors (such as the marginal product of capital). In-flation occurred whenever the central banks lowered interest rates withoutany decline in the natural rate having occurred to justify it or whenever thenatural rate of interest increased (due, e.g., to an increase in the produc-tivity of investment opportunities) without any adjustment of the interestrates controlled by central banks in response. Deflation occurred whenevera disparity was created of the opposite sign.Whatever the validity of such a non-quantity-theoretic approach for the

analysis of price-level determination under the gold standard, Wicksell’sapproach is a particularly congenial one for thinking about our presentcircumstances—a world of purely fiat currencies in which central banks ad-just their operating targets for nominal interest rates in response to per-ceived risks of inflation, but pay little if any attention to the evolution ofmonetary aggregates—to say nothing of the one toward which we may beheaded, in which monetary frictions become negligible.42 In such a world,where the concepts of money supply and demand become inapplicable,what is there to determine an equilibrium value for the general level ofmoney prices? One possible answer is the role of past prices in determining

42. As noted earlier, Wicksell’s basic exposition of his theory is for the case of a “purecredit economy.” On the non-quantity-theoretic character of Wicksell’s explanation of price-level determination, see in particular Haavelmo (1978), Leijonhufvud (1981), and Niehans(1990). Others have insisted on the compatibility ofWicksell’s analysis with a quantity-theoreticframework; see, e.g., Humphrey (2002). I do not deny the consistency of a neo-Wicksellianaccount of a price-level determination under an interest-rate rule with a standard quantity-theoretic model; see, e.g., Section 3 of Chapter 4. But I show that the existence of a well-defineddemand formoney is not essential to the logic of such an account, which is consequently equallyapplicable to a world in which money-demand relations are undefined or unstable.


current equilibrium prices, due either to wage or price stickiness or to theeffect of past prices on expectations regarding future prices (the critical fac-tor in Wicksell’s own analysis). Thus once prices have been at a certain level(for whatever arbitrary reason), this historical initial condition ties downtheir subsequent evolution, though they may subsequently drift arbitrarilyfar from that level. But probably the most important factor, in general, is theinterest-rate policy of the central bank, insofar as this responds to the evolutionof some price index. A state of affairs in which all wages and prices were10 percent higher than they presently are would not be equally possible asan equilibrium, if the observation of such a jump in the price level wouldtrigger an increase in interest rates, as called for under either a Wicksellianrule or the Taylor rule.The way in which the equilibrium price level can be determined by the

central bank’s interest-rate response to price-level variations, without anyreference to the associated fluctuations in any monetary aggregate, can beillustrated very simply. Suppose that the equilibrium real rate of interest isdetermined by real factors (such as time preference and the productivity ofcapital), in complete independence of how nominal quantitiesmay evolve,43

and let {rt } be an exogenous stochastic process for this real rate. It thenfollows that the short-term nominal interest rate it and the log price level ptmust at all times satisfy the Fisherian relation

pt = Etpt+1 + rt − it , (4.9)

assuming rational expectations on the part of the private sector. Becausert is a certain function of exogenous real factors, rather than the measuredreal rate of return, this is an equilibrium relation—the condition required forequality between aggregate saving and investment—rather than an identity.This “flexible-price IS equation” indicates how the price level that clearsthe goods market—or equivalently, that equates saving and investment—depends on the expected future price level, real factors affecting saving andinvestment, and the nominal interest rate controlled by the central bank.Now suppose that the central bank sets the short-term nominal interest

rate according to the Wicksellian rule

it = ı̄ t + φpt , (4.10)

which generalizes (4.1) in allowing for a time-varying intercept, indicatingpossible shifts over time in monetary policy. Suppose further that {̄ıt } is an-other exogenous stochastic process (i.e., determined independently of the

43. In Chapter 2, I present assumptions under which this is true in an explicit intertempo-ral equilibrium model with flexible prices.


evolution of prices), which may or may not be correlated with the exoge-nous fluctuations in the equilibrium real rate of interest. Then substituting(4.10) into (4.9) to eliminate it , one obtains a relation of the form

pt = αEtpt+1 + α(rt − ı̄ t ) (4.11)

to determine the equilibrium evolution of the price level, given the ex-ogenous processes {rt , ı̄ t }, where α ≡ 1/(1 + φ) is a coefficient satisfying0 < α < 1.In the case that {rt , ı̄ t } are bounded processes, equation (4.11) has a

unique bounded solution, obtained by “solving forward,” namely,

pt =∞∑j=0

αj+1 Et(rt+j − ı̄ t+j

). (4.12)

Thus the equilibrium price level fluctuates in a bounded interval aroundthe long-run average value

p̄ ≡ φ−1(r̄ − ı̄),

where r̄ , ı̄ are the long-run average values of rt and ı̄ t , respectively. Thisanalysis shows how a policy rule that involves no targets for any monetaryaggregate can nonetheless control the long-run price level. It also showshow the determinants of equilibrium inflation can be understood withoutany reference to the determinants of either the money supply or moneydemand—indeed, it does not matter for the analysis just presented whetherthere is any well-defined demand function for the monetary base.The account of price-level determination implied by this theory has a

strongly Wicksellian flavor. One observes from (4.12) that the equilibriumprice level at any date t is increased by either a loosening of monetarypolicy—represented by a reduction of the intercept term ı̄ t—not justified byany decline in the equilibrium real rate or by an increase in the equilibriumreal rate rt that is not matched by a tightening of policy. The proposedforward-looking model also implies that any news that allows the privatesector to forecast the future occurrence of either of these things shouldstimulate inflation immediately.In the simple model sketched here, there is no distinction of the sort that

Wicksell makes between the actual real rate of return and the natural ratethat would occur in an intertemporal equilibrium with flexible prices. InChapter 4, however, I show how one can usefully introduce such a distinc-tion, in the context of a model with sticky prices. When prices are temporar-ily sticky, the real rate of return at which borrowing and lending occurs candiffer from the natural rate of interest, just as the level of output can differ


from its natural rate; and the degree to which both occur depends on thedegree of instability of the overall price level, as it is only when the generallevel of prices is changing that price rigidity creates distortions. Equilibriumcondition (4.9) must then be replaced by a more general one, of the form

it − Etπt+1 = r nt + δ(πt , . . .), (4.13)

where r nt is the natural rate of interest (still assumed to depend only on ex-ogenous real factors) and the discrepancy δ(·) is a function of both currentand expected future inflation.44 The system consisting of conditions (4.10)and (4.13) can again be solved for a unique bounded process for the pricelevel, and the solution is of the form

pt =∞∑j=0

ψj Et(r nt+j − ı̄ t+j

)

for certain coefficients {ψj }. Thus in the more general case, it is variation inthe natural rate of interest due to real disturbances of various sorts, to theextent that such variation is not matched by corresponding adjustment ofthe central bank’s reaction function, that causes inflation variation. Just as inWicksell’s theory, real disturbances affecting desired saving and investmentare predicted to be important sources of price-level variations; and as inthat theory, the implied variation in the natural rate of interest is a usefulsummary statistic for the way in which a variety of real disturbances shouldaffect the rate of inflation.In Chapters 2 and 4, I show how a similar analysis of equilibrium inflation

determination is possible in the case of a rule like the Taylor rule. In thiscase a positive response of the interest rate to fluctuations in the inflationrate is not sufficient to guarantee a determinate equilibrium (a uniquenonexplosive equilibrium path for the inflation rate, rather than the pricelevel). It is instead necessary that the response coefficient be greater thanone, in accordance with the Taylor principle mentioned earlier. But inthat case similar results are obtained; equilibrium inflation is a function ofcurrent and expected future gaps between the natural rate of interest andthe intercept term in the Taylor rule.One finds, then, that it is possible to determine the consequences for

inflation dynamics of a given monetary policy rule when it is expressed interms of an interest-rate rule, without any need to first translate the ruleinto an implied state-contingent path for the money supply. Hence the

44. In the case of the basic neo-Wicksellian model developed in Chapter 4, δ is a functionof πt ,Etπt+1, and Etπt+2.


terms used to describe both actual central-bank policies and simple policyprescriptions in the literature summarized previously are not inappropri-ate ones. The consequences of systematic policies of these types can con-veniently be analyzed as functions of exactly the coefficients appearing inTable 1.1.While the usefulness of the neo-Wicksellian framework sketched here is

perhaps most evident in the case of an economy without monetary frictions,so that the familiar quantity-theoretic apparatus is plainly inapplicable, it isalso equally useful in the case of an economy in which monetary frictionsstill exist, at least of the modest sort that are indicated by the observed will-ingness to hold non-interest-earning currency in an advanced economy likethat of the United States today. In what I have written previously, I have notactually relied upon any assumed absence of monetary frictions, except inassuming that the equilibrium real rate of interest (or more generally, thenatural rate of interest) is independent of the evolution of nominal vari-ables. But even in the presence of transactions frictions resulting in a de-mand for base money despite its below-market rate of return, it is unlikelythat the natural rate of interest is much affected, as a quantitative matter,by variations in the rate of inflation. (The accuracy of the approximationinvolved in neglecting such effects is considered numerically in Chapters 2and 4.) Hence the approach proposed here is also appropriate for analysisof the effects of a Taylor rule in an economy like that of the United States,where changes in the Fed’s interest-rate operating target are implementedthrough adjustments in the supply of (non-interest-earning) Fed balances.The monetary frictions that create a demand for such balances are impor-tant for the size of quantity adjustment required to achieve a given changein the funds rate, but are of little significance for the effects upon outputand inflation of any given change in the path of the funds rate.Nor are the predictions of the neo-Wicksellian theory really any differ-

ent from those of a standard quantity-theoretic analysis, despite the appar-ent dissimilarity of approach. In a quantity-theoretic analysis of inflationdetermination, central importance is given to the money-demand relationthat describes desired real money balances as a function of interest ratesand other variables. However, in the case of an interest-rate rule like anyof those described earlier, the money supply varies passively so as to satisfythis relation; hence the relation places no restrictions upon the equilibriumevolution of interest rates and goods prices. Thus in such a system, the equi-librium paths of interest and prices are determined by solving equations(4.9) and (4.10), or equations (4.10) and (4.13) in the case of sticky prices,just as previously. Once one knows the equilibrium paths of interest andprices, the money-demand relation can then be used to determine the im-plied evolution of the money supply as well. But this last relation does notplay an important role in determining equilibrium inflation under such an


analysis. Moreover, insisting upon first solving for the state-contingent pathof the money supply implied by the policy rule and then deriving the equi-librium path of inflation from this along quantity-theoretic lines would bean unnecessarily roundabout procedure, given that one must first solve forthe path of prices and interest rates in order to determine the path of themoney supply.The neo-Wicksellian approach is thus clearly preferable, even granting

the existence of a well-defined, econometrically stable money-demand rela-tion, if one wishes to analyze the consequences of interest-rate rules such asthe Taylor rule. But, it might be asked, is it clear that desirable policy rulesshould belong to this class, regardless of the current popularity of such pre-scriptions? Might not a money-growth rule be preferable, in which case amore traditional quantity-theoretic approach would also be necessary in or-der to explain its effects?The results of this study suggest that the answer is no. As is shown in

Chapter 8, it is possible to derive optimal policy rules that indicate how ashort-term nominal interest-rate operating target should be set, as a func-tion of the projected evolution of inflation and the output gap, without anyreference to the paths of monetary aggregates. It is further argued that thisform of prescription has the advantage, relative to other possible character-izations of optimal policy, of being invariant under a larger class of possibleexogenous disturbances. For example, in the case of an economy with a well-defined demand for base money, it is possible to compute both the state-contingent evolution of overnight interest rates and the state-contingentevolution of the monetary base in an optimal equilibrium. However, thedesired evolution of the monetary base, even when well defined, dependsupon factors that are of little or no relevance to the desired evolution ofinterest rates, and this makes it simpler to characterize optimal policy interms of an interest-rate operating target.One such factor is the dependence of the optimal path of the mone-

tary base on changes in the transactions technology—for example, availableopportunities for substitution among alternative means of payment. Suchchanges may have significant effects on money demand in the presence of agiven interest differential between base money and other riskless assets, buthave little effect on the relations between interest rates and the incentivesfor intertemporal substitution of expenditure that determine the desiredevolution of interest rates. (In an economy where the financial system isalready highly efficient, one expects further innovations to represent move-ments from one highly efficient system to another, so that the relations be-tween interest rates and the real allocation of resources remain near thosepredicted by a model with no financial frictions; but money demand maybe greatly affected in percentage terms, as it ceases to be defined in the fric-tionless limit.) Another factor is the dependence of the optimal evolutionof the monetary base on the details of monetary policy implementation.

5. Plan of the Book 55

The desired path of money-market interest rates is largely independent ofthe rate of interest paid on the monetary base. This depends instead onthe intertemporal marginal rates of substitution, the marginal products ofreal investment implied by the desired allocation of resources, and the de-sired path for inflation. But the desired path of the monetary base dependsgreatly on whether it is assumed for institutional reasons that zero inter-est is paid on base money or whether instead the interest paid on moneyvaries when other short-term interest rates vary; for the demand for basemoney depends not on the absolute level of nominal interest rates, but onthe spread between the interest rate paid on base money and that availableon other assets.Thus even when the desired evolution of the monetary base is well de-

fined, it is more dependent on special “technical” factors than is the desiredevolution of short-term nominal interest rates. This makes a descriptionof optimal monetary policy in terms of a state-contingent money growthrate less convenient. Moreover, if, as some forecast, monetary frictions arelargely eliminated in the coming century owing to the development of elec-tronic payments media, a description of optimal policy in terms of the de-sired evolution of a monetary aggregate is likely to become awkward if notaltogether impossible. Yet a description of optimal policy in terms of theprinciples that should regulate the adjustment of an interest-rate operatingtarget should still be possible. Indeed, increasing efficiency of the financialsystem should only simplify the description of optimal policy in these terms,insofar as the arbitrage relations that connect the overnight interest rate di-rectly targeted by the central bank to other interest rates and asset pricesbecome simpler and more reliable. Hence the neo-Wicksellian frameworkproposed here directs attention to precisely those elements of themonetarytransmission mechanism that are likely to remain of fundamental impor-tance for the design of effective monetary policies in a world of increasinglyefficient financial markets and institutions.

5 Plan of the Book

Part I develops a theoretical framework that can be used to analyze theconsequences of alternative monetary policy rules in a way that takes fullaccount of the implications of forward-looking private sector behavior.Chapter 2 begins by considering price-level determination when monetarypolicy is specified by an interest-rate rule in the case of a model where, forsimplicity, prices are completely flexible and the supply of goods is givenby an exogenous endowment. This chapter demonstrates the possibility ofa coherent theory of price-level determination even in the complete ab-sence of monetary frictions—a special case that is considered repeatedlyin what follows, in order to direct attention more closely to the economicrelations that are considered to be of more fundamental importance for


the characterization of optimal policy. But it also considers price-level de-termination under an interest-rate rule in a standard optimization-basedmonetarist framework, allowing a comparison between the consequencesof monetary targeting and those of commitment to an interest-rate rule,and an analysis of the extent to which the presence of monetary frictionschanges one’s conclusions about the effects of such a rule.Chapter 3 then introduces endogenous goods supply and nominal price

and wage rigidities, so that monetary policy can affect the level of real ac-tivity as well as the inflation rate. Considerable attention is given to the mi-croeconomic foundations of the aggregate-supply relations that result fromdelays in the adjustment of prices or wages, in order to select specifications(from among those that might appear similarly consistent with economet-ric evidence) with clear behavioral interpretations that thereby allow oneto take account of the “Lucas critique.” At the same time, attention is alsopaid to the need to find a specification of the dynamic relations between realactivity and inflation that is consistent with econometric evidence regardingthe effects of identified monetary disturbances. A series of modifications ofa basic sticky-price model are introduced that can improve the model’s fitwith estimated responses on various dimensions.Chapter 4 then integrates the analysis in Chapters 2 and 3, considering

the effects of interest-rate rules in a framework where monetary policy canaffect real activity and where feedback from measures of real activity to thecentral bank’s interest-rate operating target matter for the predicted effectsof such rules. In the neo-Wicksellian framework developed here, inflationdynamics results from the interaction between real disturbances on theone hand and the central bank’s interest-rate rule on the other. Wicksell’snatural rate of interest is shown to play a central role, summarizing theeffects of a variety of real disturbances that are relevant for inflation andoutput-gap determination in the case of a class of policy rules that maybe thought of as generalized Taylor rules. The chapter also includes a firstanalysis of the consequences of such a framework for the design of desirablepolicy rules by considering the conditions under which a Taylor-like ruleshould be able to stabilize inflation and the output gap.Chapter 5 discusses further elaborations of the basic neo-Wicksellian

model, mainly with regard to aggregate-demand determination, that al-low the model to better match econometric evidence regarding the effectsof monetary policy. Various reasons are discussed for delayed effects ofinterest-rate changes on aggregate demand to differ from the immediateeffect, and then some simple examples are presented of small optimizingmodels of the U.S. monetary transmission mechanism that have been fit toU.S. time series. This discussion of empirical models is intended to motivatethe kinds of model specifications that are considered in the remainder ofthis study.

5. Plan of the Book 57

Part II then considers the optimal conduct ofmonetary policy in the lightof the theoretical framework introduced in the earlier chapters. Chapter 6begins by considering appropriate stabilization goals for monetary policy.An advantage of the derivation of the proposed model’s structural relationsfrom explicit microeconomic foundations in Part I is that it is possible toask what sort of monetary policy would best serve economic welfare, giventhe objectives and constraints of the agents whose decisions account for theobserved effects of monetary policy. Chapter 6 considers the connectionbetween the obvious measure of economic welfare in such a model—theexpected utility of the representative household—and the stabilization ofmacroeconomic aggregates such as inflation and the output gap.It is shown that a quadratic approximation to expected utility, which suf-

fices (under certain conditions) for the derivation of a linear approxima-tion to an optimal policy rule, can be expressed in terms of the expectedvalue of squared deviations of certain aggregate variables from target val-ues for those variables. The variables that are relevant and the details of thequadratic loss function that can be justified onwelfare-theoretic grounds de-pend on the microeconomic foundations of one’s model of the monetarytransmission mechanism. In particular, it is shown that different assump-tions regarding price and/or wage stickiness imply that price and/or wageinflation should enter the central bank’s loss function in different ways.Nonetheless, it is argued that price stability, suitably interpreted—for ex-ample, quite possibly in terms of an index that includes wages as well as theprices of final goods and services—should be an important consideration,though not necessarily the only one, in the selection of a monetary pol-icy rule. Grounds for inclusion of output-gap stabilization and interest-ratestabilization objectives in the loss function as well are considered; but it isargued that in practice, these additional concerns are not likely to justifyeither an average rate of inflation much greater than zero or substantialvariability in the rate of inflation in response to shocks.Chapter 7 then considers the optimal state-contingent evolution of infla-

tion, output, and interest rates in response to real disturbances of varioussorts, from the point of view of the sort of loss function argued for inChapter6 and in the context of a forward-looking model of the monetary transmis-sion mechanism of the kind developed in Part I. An important general issuetreated in this chapter is the way in which optimal control techniques mustbe adapted in the case of control of a forward-looking system. The responsesto shocks under an optimal commitment are distinguished from the equilib-rium responses under discretionary optimization by the central bank. Par-ticular attention is given to the fact that in general, optimal responses will behistory dependent in a way that is inconsistent with any purely forward-lookingdecision procedure for monetary policy. Alternative approaches to intro-ducing the desired sort of history dependence into the conduct of policy


are surveyed. The one that is emphasized in this study is the possibility ofcommitment to a policy rule that is history dependent in the desired way.Commitment to a targeting rule, such as a flexible inflation target, is shownto be an especially desirable way of formulating such a policy commitment.Finally, Chapter 8 considers the problem of choice of a policy rule to

implement the desired state-contingent evolution of inflation, output, andinterest rates, as derived in Chapter 7. From the standpoint taken here, thisproblem of implementation of the desired equilibrium is a nontrivial part ofthe characterization of optimal policy. The mapping from the history ofexogenous disturbances to the desired overnight interest rate at any pointin time is not a suitable description of an optimal policy rule, for reasonstaken up in this chapter. Instead, it is argued that a more suitable policyprescription should relate the instrument setting to the evolution (observedor projected) of endogenous variables such as inflation and the outputgap, as in the proposals mentioned earlier. A general method is describedfor constructing optimal policy rules of this form in the case of a fairlygeneral class of log-linear structural models and quadratic loss functions.The method is then applied to several of the simple optimizing models ofthe monetary transmission mechanism developed in previous chapters.It is shown that optimal rules can easily take the form of generalized

Taylor rules or of target criteria for a forecast-targeting procedure like thatused at the Bank of England. However, even in the case of fairly simplemodels of the transmission mechanism, the optimal rules are somewhatdifferent from the proposals described earlier. While there is a fairly clearlogic for rules that respond to (and perhaps only to) variations in inflationand in the output gap, the theoretically appropriate measures of inflationand of the output gap may not be the ones used in the characterizationsabove of current central-bank behavior. Moreover, the optimal rules that Iobtain are also typically different in their dynamic specifications. Optimalrules are history dependent in ways other than those of the classic Taylorrule or familiar descriptions of inflation-forecast targeting; and while theymay well be more forward looking than the classic Taylor rule, in all ofthe calibrated examples they are considerably less forward looking than theprocedures currently used at the inflation-targeting central banks.Conclusions about the precise content of an optimal policy rule depend,

of course, on the details of one’s model of the transmission mechanism,and I do not attempt here to reach final conclusions in that regard. Theanswer is likely to be somewhat different for different countries in any event.My more important goal is to provide a method that individual centralbanks can use in order to choose sensible systematic policies on the basisof their own research on the nature of the transmission mechanism in theirrespective economies. It is hoped that the present volume can provide usefulguidelines for such an inquiry.

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Princeton University - The Return of Monetary Rulesassets.press.princeton.edu/chapters/s7603.pdfCHAPTER 1 The Return of Monetary Rules Ifitwereinourpowertoregulatecompletelythepricesystemofthe